Pith. sign in

REVIEW 3 major objections 5 minor 170 references

Chemical potential of the warm dense electron gas from ab initio path integral Monte Carlo simulations

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper uses two independent ab initio path integral Monte Carlo routes to compute the exchange-correlation chemical potential of the warm dense uniform electron gas and finds it agrees with the standard free-energy parametrization to…

desk verdict First direct PIMC chemical potentials for the warm dense UEG, with a believable 0.5% cross-check of GDSMFB; extrapolation caveat aside, this deserves a referee. read the letter →

arxiv 2412.15777 v1 pith:LJDE27YS submitted 2024-12-20 physics.chem-ph cond-mat.quant-gasphysics.plasm-ph

Tobias Dornheim , Michael Bonitz , Zhandos Moldabekov , Sebastian Schwalbe , Panagiotis Tolias , Jan Vorberger This is my paper · ORCID
classification physics.chem-phcond-mat.quant-gasphysics.plasm-ph
keywords warmdensematteruniformelectrongaschemicalpotentialpathintegralMonteCarloexchange-correlationfreeenergyfinite-sizescalingthermodynamiclimitequationofstate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the chemical potential of the warm dense uniform electron gas can be computed directly and exactly from path integral Monte Carlo simulations, without external finite-size corrections, and that this new route cross-validates current state-of-the-art equation-of-state parametrizations. Two independent estimators are used: the difference of free energies from the recently introduced eta-ensemble approach, and a histogram estimator that reads the chemical potential off the ratio of partition functions for N and N+1 particles in a single simulation. Both agree. Exploiting the known inverse-linear dependence of the exchange-correlation chemical potential on particle number, the authors extrapolate to the thermodynamic limit and find agreement with the Groth et al. exchange-correlation free-energy parametrization within about 0.5% for rs <= 20, supporting that parametrization and opening a derivative-free route to equations of state.

What carries the argument

The central object is the exchange-correlation chemical potential $\mu_\textnormal{xc}(N,V,\beta)$, obtained either as a free-energy difference or as $-\frac{1}{\beta}\log[Z(N+1)/Z(N)]$. The argument is carried by two mechanisms: (i) the $\eta$-ensemble estimator, which connects the interacting Fermi system to an ideal Bose reference through a coupling parameter $\eta$ and an average sign factor $S$, giving the free energy without thermodynamic integration; and (ii) the particle-number histogram estimator, which evaluates the ratio of canonical partition functions in a generalized grand-canonical simulation with a Gaussian weight on the particle number. The known asymptotic scaling $\Delta\mu_\textnormal{xc} = \frac{1}{2N}\frac{\partial P}{\partial n}\{1 - \frac{1}{\beta}[(\partial n/\partial P) + n(\partial^2 P/\partial n^2)(\partial n/\partial P)^2]\} + O(N^{-2})$ then provides the thermodynamic-limit extrapolation. The decomposition $\mu = \mu_{B_0} + \Delta\mu_{B_0,B} + \Delta\mu_{B,F}$ absorbs quantum statistics into a small, almost $N$-independent correction.

What would settle it

Run the histogram estimator for $r_s = 1$, $\Theta = 2$ at $N = 14, 34, 66, 120, 200$ and fit the raw fermionic data alone, without the bosonic correction, to a line in $1/N$; if the intercept shifts by more than about 0.5% of $\mu_\textnormal{xc}$ relative to GDSMFB, the linear scaling is not yet converged in this range. Alternatively, resolve the Fermi-minus-Bose correction $\Delta\mu_{B,F}$ at $N = 14$ and $N = 200$: a significant $N$-dependence would bias the thermodynamic-limit values in Table I.

Watch

Extended reading notes

Core claim

The central claim is that the exchange-correlation contribution to the chemical potential of the uniform electron gas at warm dense matter conditions, computed from path integral Monte Carlo in the thermodynamic limit, matches the GDSMFB parametrization (a widely used fit of the exchange-correlation free energy by Groth and co-workers) to within about 0.5% for rs <= 20, with the largest deviation of about 1% at rs = 100, outside GDSMFB's nominal range. This is a cross-validation from an independent route because it avoids the thermodynamic integration and the semi-analytical finite-size corrections used to construct the parametrization. The paper also establishes that the quantum statistics correction (Fermi minus Bose) is nearly independent of the number of simulated electrons for the studied conditions, so accurate bosonic simulations can be corrected with small-system estimates, and that the histogram estimator is more efficient than the direct free-energy difference route.

Load-bearing premise

The thermodynamic-limit extrapolation assumes that the exchange-correlation chemical potential already follows its asymptotic linear-in-$1/N$ falloff for systems of 20 to 200 electrons, and that the Fermi-minus-Bose statistics correction is essentially independent of particle number, so a correction computed with 14 electrons applies at all larger $N$.

Editorial extensions

If this is right

  • The GDSMFB and, by extension, the corrected KSDT free-energy parametrizations are independently confirmed at the derivative level for $r_s \le 20$, meaning thermal density functional theory calculations that use them inherit a chemical potential accurate to roughly 0.5%.
  • The extrapolated $\mu_\textnormal{xc}$ values in Table I form a new benchmark dataset for future equation-of-state parametrizations, particularly where derivatives of the free energy are needed.
  • The histogram estimator combined with the bosonic-correction scheme gives reliable chemical potentials for up to about 200 electrons without the fermion sign problem dominating the error, providing a template for ab initio studies of real warm dense matter such as hydrogen.
  • Through the Gibbs-Duhem relation, the new chemical potential data open a route to the isothermal compressibility from four adjacent state-point simulations, an alternative to second-derivative free-energy routes.
  • The direct access to the chemical potential gives addition energies and stability information for warm dense systems without reference to density functional theory reference energies or pseudopotential shifts.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the 0.5% agreement holds over a broader grid of state points, derivative-level artifacts such as oscillations in heat capacities reported for GDSMFB or corrKSDT may be blamed on the free-energy functional form rather than on the underlying PIMC data, making the chemical potential a useful diagnostic for functional quality.
  • The near-$N$-independence of the Fermi-minus-Bose correction suggests that a bosonic-reference strategy could accelerate PIMC for other fermionic warm dense systems, but this needs testing at lower temperatures and stronger degeneracy, where permutation cycles and the sign problem grow.
  • Combining the histogram estimator with $\xi$-extrapolation techniques could reach several hundred electrons at mild degeneracy, allowing a direct check of whether the linear $1/N$ scaling used here is fully converged in the simulated range.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents ab initio path integral Monte Carlo (PIMC) results for the chemical potential of the warm dense uniform electron gas (UEG). Two independent routes are used: direct free-energy differences from the η-ensemble and a histogram estimator based on simulations with a varying particle number. The chemical potential is decomposed into an ideal Bose term, a bosonic interaction term, and a quantum statistics correction, and the XC contribution is extrapolated to the thermodynamic limit using a linear fit in 1/N motivated by Eq. (26). The authors report agreement with the GDSMFB free-energy parametrization to within about 0.5% for rs ≤ 20 and provide a table of TDL-extrapolated μ_xc values.

Significance. If the systematic uncertainties are controlled, this is a valuable independent constraint on finite-T UEG free-energy functionals, since μ_xc is a derivative quantity that is more sensitive than the free energy itself. The strengths of the paper are the two independent estimators that agree within error bars, the validation of the histogram estimator against the exact ideal Fermi gas, the use of the theoretically predicted 1/N scaling without external finite-size corrections, and the open-source ISHTAR code. The TDL data in Table I and the proposed Gibbs–Duhem route to the isothermal compressibility are useful contributions. However, the central cross-validation claim of ~0.5% precision depends on systematic errors in the thermodynamic-limit extrapolation and in the quantum-statistics correction that are not quantitatively established.

major comments (3)
  1. [§III B, Eq. (26), Sec. IV] The extrapolation to the thermodynamic limit presumes that μ_xc(N) is linear in 1/N for N≥20 and that the O(N^{-2}) term is negligible. The paper itself states in Sec. IV that a residual second-order effect 'might also explain the observed small deviations', but no estimate of its magnitude is given. At the most demanding state point (rs=1, Θ=2), the finite-size effect at N=14 is roughly half of μ_xc in the TDL, so the fit range begins at N=20 where the correction is still large; a curvature of only a few tenths of a percent at N=20 would shift the intercept by an amount comparable to the claimed 0.5% agreement. Please quantify the O(N^{-2}) contribution, for example by including a quadratic term in the fit or by comparing fits with and without the N=14 point, and propagate the resulting uncertainty into Table I.
  2. [§III B, Figs. 3–5] The treatment of the quantum statistics correction Δμ_B,F is described inconsistently. In Fig. 3, a constant correction computed at N=14 is added to bosonic results; in Fig. 4, an 'empirical linear model' for Δμ_F,B(N) is fitted; and the Fig. 5 caption indicates a correction that depends on N. If a constant N=14 value is applied to all N up to 200, any weak N-dependence of Δμ_B,F introduces a bias not included in the reported error bars; if a linear fit is used instead, the slope and its uncertainty must be reported. The paper should state exactly which correction was used to produce Table I, display the fitted Δμ_B,F(N) for each state point, and test whether the N-dependence is statistically significant.
  3. [§III C, Table I] The central claim of agreement with GDSMFB to within ~0.5% at rs=1,2 for Θ=2 rests on TDL intercepts whose statistical errors in Table I are an order of magnitude smaller (for example, 0.1–0.2%). The systematic uncertainties identified in the two preceding comments therefore dominate the comparison. Since the authors explicitly state that they cannot conclusively resolve the origin of the deviations, the cross-validation claim is not yet established at the stated precision. Please provide a conservative systematic error budget for the TDL extrapolation and the statistics correction, or soften the claimed precision accordingly.
minor comments (5)
  1. [Eq. (11)] Equation (11) as printed contains a garbled sequence of symbols; the definition of Δμ_B0,B should be written out cleanly so that the decomposition is unambiguous.
  2. [Sec. III C] The word 'parmetrization' should be 'parametrization'.
  3. [Eqs. (20)–(21)] The histogram estimator depends on the free parameters μ_GC and σ_N; the paper states σ_N=0.6 is a good choice but does not report a sensitivity study. A brief statement of robustness with respect to these parameters would be helpful.
  4. [Eqs. (25)–(26)] The symbol Δ is used for both finite-size corrections (e.g., Δμ_0) and the quantum statistics contribution Δμ_B,F; the notation is confusing in places and should be distinguished more clearly.
  5. [Fig. 3] The yellow squares, obtained by adding the finite-size-corrected non-interacting contribution, change the sign of the N-dependence relative to the raw data; a sentence explaining this behavior would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the PIMC chemical potential is computed directly from partition-function ratios and free-energy differences, with the GDSMFB parametrization serving only as a comparison reference; the residual TDL extrapolation concern is a precision caveat, not a construction-level equivalence.

full rationale

The paper's central claim is that two independent PIMC estimators of the chemical potential, the direct free-energy difference via the eta-ensemble and the particle-number histogram estimator, agree with each other and with the GDSMFB free-energy parametrization at the roughly 0.5% level. Neither estimator is defined in terms of GDSMFB, nor is any GDSMFB-derived quantity used as input to the PIMC data. The histogram estimator is benchmarked against the exact canonical chemical potential of the ideal Fermi gas in Fig. 1, and the two estimators are cross-checked against each other in Fig. 3. The TDL extrapolation uses the known 1/N asymptotic form of the XC chemical potential from external references [127,128], and the fitted lines are applied to PIMC data, not to the reference parametrization. The GDSMFB comparison enters only as a reference curve, a normalization convention in Fig. 4, and a discussion target. Although GDSMFB and the eta-ensemble method originate from the same research group, the present PIMC results are new simulations with exact benchmarks and independent estimators, so the author overlap does not make the agreement circular. The paper explicitly acknowledges in Sec. III C that a small residual second-order term in the TDL extrapolation 'might also explain the observed small deviations' and that this cannot be conclusively resolved. That is an honest limitation on the precision of the cross-validation, but it is not a case of a prediction being forced by construction or by self-citation. The agreement with GDSMFB is not enforced by the method; both routes to mu are direct statistical estimates from the simulated partition functions.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameter sigma_N is an algorithmic choice in the histogram estimator. The key assumptions are the standard Ewald treatment, the 1/N scaling law from the literature, and the empirical N-independence of the quantum statistics correction.

free parameters (1)
  • sigma_N = 0.6
    Width of the Gaussian weight function W(N') in the generalized grand-canonical histogram estimator (Eq. 20). Chosen empirically to balance sampling efficiency and bias; enters the final expression Eq. (21) as a known constant, so it does not bias the estimate of mu.
assumptions (5)
  • standard math The canonical ensemble chemical potential is defined by mu(N,V,beta) = F(N+1) - F(N).
    Sec. II A, Eq. (2). Standard thermodynamic relation.
  • domain assumption The Ewald pair interaction with neutralizing background is the appropriate interaction for an added electron in a periodic simulation cell.
    Sec. II A: the authors choose the neutralized Ewald potential based on classical results by Bakhshandeh and Levin [126]; this choice affects finite-size behavior, though the TDL should be independent.
  • standard math The ideal Bose/Fermi canonical partition functions are computed via the recursion relation of Ref. [111], Eq. (6).
    Sec. II C. Accepted result; used as reference for the eta-ensemble.
  • domain assumption The exchange-correlation part of the chemical potential scales as Delta_mu_xc(N) = C/N + O(N^-2) with C given by Eq. (26) from Refs. [127,128].
    Sec. III B. This is the basis for the linear extrapolation to the TDL; the paper empirically confirms the linear behavior for N >= 20 at the studied state points.
  • ad hoc to paper The quantum statistics correction Delta_mu_{B,F}(N) is nearly independent of N and can be estimated from small systems (N=14) and applied to bosonic PIMC results at all larger N.
    Sec. III B, Fig. 4. The paper shows a weak N-dependence for the tested cases and uses an empirical linear model for the correction. This is the main load-bearing modeling choice for the efficient TDL extrapolation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Chemical potential of the warm dense electron gas from ab initio path integral Monte Carlo simulations." pith.science (2026). https://pith.science/paper/LJDE27YS

@misc{pith2026241215777,
  author       = {Pith},
  title        = {Pith review of: Chemical potential of the warm dense electron gas from ab initio path integral Monte Carlo simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LJDE27YS}},
  note         = {Machine review of arXiv:2412.15777}
}
abstract

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulation results for the chemical potential of the warm dense uniform electron gas (UEG), spanning a broad range of densities and temperatures. This is achieved by following two independent routes, i) based on the direct estimation of the free energy [Dornheim \emph{et al.}, arXiv:2407.01044] and ii) using a histogram estimator in PIMC simulations with a varying number of particles. We empirically confirm the expected inverse linear dependence of the exchange--correlation (XC) part of the chemical potential on the simulated number of electrons, which allows for a reliable extrapolation to the thermodynamic limit without the necessity for an additional finite-size correction. We find very good agreement (within $\Delta\mu_\textnormal{xc}\lesssim0.5\%$) with the previous parametrization of the XC-free energy by Groth \emph{et al.}~[\emph{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)], which constitutes an important cross validation of current state-of-the-art UEG equations of state. In addition to being interesting in its own right, our study constitutes the basis for the future PIMC based investigation of the chemical potential of real warm dense matter systems starting with hydrogen.

Figures

Figures reproduced from arXiv: 2412.15777 by the authors.

Figure 1
Figure 1. FIG. 1. Top panel: The dependence of the chemical potential [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The average sign [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Left panel: The dependence of the chemical potential, for the unpolarized UEG with [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Extrapolation of the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Top (bottom) [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

170 extracted references · 66 canonical work pages

  1. [1]

    Graziani, M

    F. Graziani, M. P. Desjarlais, R. Redmer, and S. B. Trickey, eds., Frontiers and Challenges in Warm Dense Matter (Springer, International Publishing, 2014)

    2014

  2. [2]

    Ab initio simulation of warm dense matter,

    M. Bonitz, T. Dornheim, Zh. A. Moldabekov, S. Zhang, P. Hamann, H. K¨ ahlert, A. Filinov, K. Ramakrishna, and J. Vorberger, “Ab initio simulation of warm dense matter,” Phys. Plasmas 27, 042710 (2020)

    2020

  3. [3]

    Drake, High-Energy-Density Physics: Founda- tion of Inertial Fusion and Experimental Astrophysics, Graduate Texts in Physics (Springer International Pub- lishing, 2018)

    R.P. Drake, High-Energy-Density Physics: Founda- tion of Inertial Fusion and Experimental Astrophysics, Graduate Texts in Physics (Springer International Pub- lishing, 2018)

    2018

  4. [4]

    Toward First-principles based simulations of dense hydrogen,

    M. Bonitz, J. Vorberger, M. Bethkenhagen, M. B¨ ohme, D.M. Ceperley, A. Filinov, T. Gawne, F. Graziani, G. Gregori, P. Hamann, S.B. Hansen, M. Holzmann, S.X. Hu, H. K¨ ahlert, V. Karasiev, U. Kleinschmidt, L. Kordts, C. Makait, B. Militzer, Z.A. Moldabekov, C. Pierleoni, M. Preising, K. Ramakrishna, R. Redmer, S. Schwalbe, P. Svensson, and T. Dornheim, “T...

    2024

  5. [5]

    Progress in warm dense matter study with applications to planetology,

    Alessandra Benuzzi-Mounaix, St´ ephane Mazevet, Alessandra Ravasio, Tommaso Vinci, Adrien De- noeud, Michel Koenig, Nourou Amadou, Erik Bram- brink, Floriane Festa, Anna Levy, Marion Harmand, St´ ephanie Brygoo, Gael Huser, Vanina Recoules, Johan Bouchet, Guillaume Morard, Fran¸ cois Guyot, Thibaut de Resseguier, Kohei Myanishi, Norimasa Ozaki, Fabien Dor...

    2014

  6. [6]

    Hydrogen-helium mixtures in the interiors of giant planets,

    J. Vorberger, I. Tamblyn, B. Militzer, and S. A. Bonev, “Hydrogen-helium mixtures in the interiors of giant planets,” Phys. Rev. B 75, 024206 (2007)

    2007

  7. [7]

    Ab initio equations of state for hydrogen (h-reos.3) and helium (he-reos.3) and their implications for the interior of brown dwarfs,

    A. Becker, W. Lorenzen, J. J. Fortney, N. Nettelmann, M. Sch¨ ottler, and R. Redmer, “Ab initio equations of state for hydrogen (h-reos.3) and helium (he-reos.3) and their implications for the interior of brown dwarfs,” As- trophys. J. Suppl. Ser 215, 21 (2014)

    2014

  8. [8]

    Current challenges in the physics of white dwarf stars,

    Didier Saumon, Simon Blouin, and Pier-Emmanuel Tremblay, “Current challenges in the physics of white dwarf stars,” Phys. Rep. 988, 1–63 (2022)

    2022

Show all 170 references
  1. [9]

    Nanosecond formation of diamond and lonsdaleite by shock com- pression of graphite,

    D. Kraus, A. Ravasio, M. Gauthier, D. O. Gericke, J. Vorberger, S. Frydrych, J. Helfrich, L. B. Fletcher, G. Schaumann, B. Nagler, B. Barbrel, B. Bachmann, E. J. Gamboa, S. G¨ ode, E. Granados, G. Gregori, H. J. Lee, P. Neumayer, W. Schumaker, T. D¨ oppner, R. W. Falcone, S. H...

    2016

  2. [10]

    Plasmon-induced hot carrier science and tech- nology,

    Mark L. Brongersma, Naomi J. Halas, and Peter Nord- lander, “Plasmon-induced hot carrier science and tech- nology,” Nature Nanotechnology 10, 25–34 (2015)

    2015

  3. [11]

    Physics principles of inertial confinement fu- sion and U.S. program overview,

    O. A. Hurricane, P. K. Patel, R. Betti, D. H. Froula, 13 S. P. Regan, S. A. Slutz, M. R. Gomez, and M. A. Sweeney, “Physics principles of inertial confinement fu- sion and U.S. program overview,” Rev. Mod. Phys. 95, 025005 (2023)

    2023

  4. [12]

    Inertial-confinement fu- sion with lasers,

    R. Betti and O. A. Hurricane, “Inertial-confinement fu- sion with lasers,” Nature Physics 12, 435–448 (2016)

    2016

  5. [13]

    First-principles equation-of-state table of deuterium for inertial confinement fusion applications,

    S. X. Hu, B. Militzer, V. N. Goncharov, and S. Skupsky, “First-principles equation-of-state table of deuterium for inertial confinement fusion applications,” Phys. Rev. B 84, 224109 (2011)

    2011

  6. [14]

    Future for inertial- fusion energy in Europe: a roadmap,

    Dimitri Batani, Arnaud Cola ¨ ıtis, Fabrizio Consoli, Colin N. Danson, Leonida Antonio Gizzi, Javier Hon- rubia, Thomas K¨ uhl, Sebastien Le Pape, Jean-Luc Miquel, Jose Manuel Perlado, et al., “Future for inertial- fusion energy in Europe: a roadmap,” High Power Laser Sci. Eng...

    2023

  7. [15]

    Experimental methods for warm dense matter research,

    K. Falk, “Experimental methods for warm dense matter research,” High Power Laser Sci. Eng 6, e59 (2018)

    2018

  8. [16]

    The National Ignition Facility: Usher- ing in a new age for high energy density science,

    E. I. Moses, R. N. Boyd, B. A. Remington, C. J. Keane, and R. Al-Ayat, “The National Ignition Facility: Usher- ing in a new age for high energy density science,” Phys. Plasmas 16, 041006 (2009)

    2009

  9. [17]

    Observing the onset of pressure-driven K-shell delocalization,

    T. D¨ oppner, M. Bethkenhagen, D. Kraus, P. Neu- mayer, D. A. Chapman, B. Bachmann, R. A. Bag- gott, M. P. B¨ ohme, L. Divol, R. W. Falcone, L. B. Fletcher, O. L. Landen, M. J. MacDonald, A. M. Saun- ders, M. Sch¨ orner, P. A. Sterne, J. Vorberger, B. B. L. Witte, A. Yi, R. Re...

    2023

  10. [18]

    The collid- ing planar shocks platform to study warm dense matter at the National Ignition Facility,

    M. J. MacDonald, C. A. Di Stefano, T. D¨ oppner, L. B. Fletcher, K. A. Flippo, D. Kalantar, E. C. Merritt, S. J. Ali, P. M. Celliers, R. Heredia, S. Vonhof, G. W. Collins, J. A. Gaffney, D. O. Gericke, S. H. Glenzer, D. Kraus, A. M. Saunders, D. W. Schmidt, C. T. Wil- son, R. ...

    2023

  11. [19]

    Linac Coherent Light Source: The first five years,

    Christoph Bostedt, S´ ebastien Boutet, David M. Fritz, Zhirong Huang, Hae Ja Lee, Henrik T. Lemke, Aymeric Robert, William F. Schlotter, Joshua J. Turner, and Garth J. Williams, “Linac Coherent Light Source: The first five years,” Rev. Mod. Phys. 88, 015007 (2016)

    2016

  12. [20]

    Mat- ter under extreme conditions experiments at the Linac Coherent Light Source,

    S H Glenzer, L B Fletcher, E Galtier, B Nagler, R Alonso-Mori, B Barbrel, S B Brown, D A Chap- man, Z Chen, C B Curry, F Fiuza, E Gamboa, M Gau- thier, D O Gericke, A Gleason, S Goede, E Granados, P Heimann, J Kim, D Kraus, M J MacDonald, A J Mackinnon, R Mishra, A Ravasio, C ...

    2016

  13. [21]

    The Role of the Laboratory for Laser Energetics in the National Ignition Facility Project,

    J. M. Soures, S. J. Loucks, R. L. McCrory, C. P. Verdon, A. Babushkin, R. E. Bahr, T. R. Boehly, R. Boni, D. K. Bradley, D. L. Brown, J. A. Delettrez, R. S. Craxton, W. R. Donaldson, R. Epstein, R. Gram, D. R. Hard- ing, P. A. Jaanimagi, S. D. Jacobs, K. Kearney, R. L. Keck, J...

    1996

  14. [22]

    Observations of plasmons in warm dense matter,

    S. H. Glenzer, O. L. Landen, P. Neumayer, R. W. Lee, K. Widmann, S. W. Pollaine, R. J. Wallace, G. Gre- gori, A. H¨ oll, T. Bornath, R. Thiele, V. Schwarz, W.- D. Kraeft, and R. Redmer, “Observations of plasmons in warm dense matter,” Phys. Rev. Lett. 98, 065002 (2007)

    2007

  15. [23]

    The Laser Mega- Joule : LMJ, PETAL status and Program Overview,

    J-L Miquel, C Lion, and P Vivini, “The Laser Mega- Joule : LMJ, PETAL status and Program Overview,” J. Phys.: Conf. Ser. 688, 012067 (2016)

    2016

  16. [24]

    Pho- ton Beam Transport and Scientific Instruments at the European XFEL,

    Thomas Tschentscher, Christian Bressler, Jan Gr¨ unert, Anders Madsen, Adrian P. Mancuso, Michael Meyer, Andreas Scherz, Harald Sinn, and Ulf Zastrau, “Pho- ton Beam Transport and Scientific Instruments at the European XFEL,” Appl. Sci. 7, 592 (2017)

    2017

  17. [25]

    X-ray Thomson scatter- ing in high energy density plasmas,

    S. H. Glenzer and R. Redmer, “X-ray Thomson scatter- ing in high energy density plasmas,” Rev. Mod. Phys 81, 1625 (2009)

    2009

  18. [26]

    Sheffield, D

    J. Sheffield, D. Froula, S.H. Glenzer, and N.C. Luh- mann, Plasma Scattering of Electromagnetic Radiation: Theory and Measurement Techniques(Elsevier Science, 2010)

    2010

  19. [27]

    Ultrabright X-ray laser scattering for dy- namic warm dense matter physics,

    L. B. Fletcher, H. J. Lee, T. D¨ oppner, E. Galtier, B. Na- gler, P. Heimann, C. Fortmann, S. LePape, T. Ma, M. Millot, A. Pak, D. Turnbull, D. A. Chapman, D. O. Gericke, J. Vorberger, T. White, G. Gregori, M. Wei, B. Barbrel, R. W. Falcone, C.-C. Kao, H. Nuhn, J. Welch, U. Za...

    2015

  20. [28]

    Theoretical model of x-ray scattering as a dense matter probe,

    G. Gregori, S. H. Glenzer, W. Rozmus, R. W. Lee, and O. L. Landen, “Theoretical model of x-ray scattering as a dense matter probe,” Phys. Rev. E 67, 026412 (2003)

    2003

  21. [29]

    Evidence of free-bound transitions in warm dense matter and their impact on equation-of-state mea- surements,

    Maximilian P. B¨ ohme, Luke B. Fletcher, Tilo D¨ oppner, Dominik Kraus, Andrew D. Baczewski, Thomas R. Preston, Michael J. MacDonald, Frank R. Graziani, Zhandos A. Moldabekov, Jan Vorberger, and Tobias Dornheim, “Evidence of free-bound transitions in warm dense matter and thei...

    2023 arXiv

  22. [30]

    Electron-Ion Tempera- ture Relaxation in Warm Dense Hydrogen Observed With Picosecond Resolved X-Ray Scattering,

    L. B. Fletcher, J. Vorberger, W. Schumaker, C. Ruyer, S. Goede, E. Galtier, U. Zastrau, E. P. Alves, S. D. Baal- rud, R. A. Baggott, B. Barbrel, Z. Chen, T. D¨ oppner, M. Gauthier, E. Granados, J. B. Kim, D. Kraus, H. J. Lee, M. J. MacDonald, R. Mishra, A. Pelka, A. Rava- sio,...

    2022

  23. [31]

    Free-Electron X-Ray Laser Measurements of Collisional-Damped Plasmons in Isochorically Heated Warm Dense Matter,

    P. Sperling, E. J. Gamboa, H. J. Lee, H. K. Chung, E. Galtier, Y. Omarbakiyeva, H. Reinholz, G. R¨ opke, U. Zastrau, J. Hastings, L. B. Fletcher, and S. H. Glenzer, “Free-Electron X-Ray Laser Measurements of Collisional-Damped Plasmons in Isochorically Heated Warm Dense Matter...

    2015

  24. [32]

    Accurate temperature di- agnostics for matter under extreme conditions,

    Tobias Dornheim, Maximilian B¨ ohme, Dominik Kraus, 14 Tilo D¨ oppner, Thomas R. Preston, Zhandos A. Mold- abekov, and Jan Vorberger, “Accurate temperature di- agnostics for matter under extreme conditions,” Nature Communications 13, 7911 (2022)

    2022

  25. [33]

    Imaginary-time cor- relation function thermometry: A new, high-accuracy and model-free temperature analysis technique for x-ray Thomson scattering data,

    Tobias Dornheim, Maximilian P. B¨ ohme, David A. Chapman, Dominik Kraus, Thomas R. Preston, Zhan- dos A. Moldabekov, Niclas Schl¨ unzen, Attila Cangi, Tilo D¨ oppner, and Jan Vorberger, “Imaginary-time cor- relation function thermometry: A new, high-accuracy and model-free tem...

    2023

  26. [34]

    X-ray Thomson scattering absolute intensity from the f-sum rule in the imaginary- time domain,

    T. Dornheim, T. D¨ oppner, A. D. Baczewski, P. Tolias, M. P. B¨ ohme, Zh. A. Moldabekov, Th. Gawne, D. Ran- jan, D. A. Chapman, M. J. MacDonald, Th. R. Preston, D. Kraus, and J. Vorberger, “X-ray Thomson scattering absolute intensity from the f-sum rule in the imaginary- time ...

    2024

  27. [35]

    Model-free Rayleigh weight from x-ray Thomson scattering measurements,

    Tobias Dornheim, Hannah M. Bellenbaum, Mandy Bethkenhagen, Stephanie B. Hansen, Maximilian P. B¨ ohme, Tilo D¨ oppner, Luke B. Fletcher, Thomas Gawne, Dirk O. Gericke, Sebastien Hamel, Dominik Kraus, Michael J. MacDonald, Zhandos A. Mold- abekov, Thomas R. Preston, Ronald Redm...

    2024 arXiv

  28. [36]

    Revealing non- equilibrium and relaxation in laser heated matter,

    Jan Vorberger, Thomas R. Preston, Nikita Medvedev, Maximilian P. B¨ ohme, Zhandos A. Moldabekov, Do- minik Kraus, and Tobias Dornheim, “Revealing non- equilibrium and relaxation in laser heated matter,” Phys. Lett. A 499, 129362 (2024)

    2024

  29. [37]

    X-ray Thomson scat- tering spectra from density functional theory molecular dynamics simulations based on a modified Chihara for- mula,

    Maximilian Sch¨ orner, Mandy Bethkenhagen, Tilo D¨ oppner, Dominik Kraus, Luke B. Fletcher, Siegfried H. Glenzer, and Ronald Redmer, “X-ray Thomson scat- tering spectra from density functional theory molecular dynamics simulations based on a modified Chihara for- mula,” Phys. ...

    2023

  30. [38]

    Unraveling electronic cor- relations in warm dense quantum plasmas,

    Tobias Dornheim, Tilo D¨ oppner, Panagiotis Tolias, Maximilian B¨ ohme, Luke Fletcher, Thomas Gawne, Frank Graziani, Dominik Kraus, Michael MacDonald, Zhandos Moldabekov, Sebastian Schwalbe, Dirk Ger- icke, and Jan Vorberger, “Unraveling electronic cor- relations in warm dense...

    2024 arXiv

  31. [39]

    Ultrahigh resolution x- ray Thomson scattering measurements at the European X-ray Free Electron Laser,

    Thomas Gawne, Zhandos A. Moldabekov, Oliver S. Humphries, Karen Appel, Carsten Baehtz, Victorien Bouffetier, Erik Brambrink, Attila Cangi, Sebastian G¨ ode, Zuzana Konˆ opkov´ a, Mikako Makita, Mikhail Mishchenko, Motoaki Nakatsutsumi, Kushal Ramakr- ishna, Lisa Randolph, Seba...

    2024

  32. [40]

    Electron dynamics in extended systems within real-time time-dependent density-functional theory,

    Alina Kononov, Cheng-Wei Lee, Tatiane Pereira dos Santos, Brian Robinson, Yifan Yao, Yi Yao, Xavier Andrade, Andrew David Baczewski, Emil Constanti- nescu, Alfredo A. Correa, Yosuke Kanai, Normand Modine, and Andr´ e Schleife, “Electron dynamics in extended systems within real...

    2022

  33. [41]

    Equa- tion of state measurements of warm dense carbon using laser-driven shock and release technique,

    K. Falk, E. J. Gamboa, G. Kagan, D. S. Montgomery, B. Srinivasan, P. Tzeferacos, and J. F. Benage, “Equa- tion of state measurements of warm dense carbon using laser-driven shock and release technique,” Phys. Rev. Lett. 112, 155003 (2014)

    2014

  34. [42]

    Self-consistent measurement of the equation of state of liquid deuterium,

    K. Falk, S.P. Regan, J. Vorberger, M.A. Barrios, T.R. Boehly, D.E. Fratanduono, S.H. Glenzer, D.G. Hicks, S.X. Hu, C.D. Murphy, P.B. Radha, S. Rothman, A.P. Jephcoat, J.S. Wark, D.O. Gericke, and G. Gregori, “Self-consistent measurement of the equation of state of liquid deute...

    2012

  35. [43]

    Recent progress in the theory and simulation of strongly corre- lated plasmas: phase transitions, transport, quantum, and magnetic field effects,

    Torben Ott, Hauke Thomsen, Jan Willem Abra- ham, Tobias Dornheim, and Michael Bonitz, “Recent progress in the theory and simulation of strongly corre- lated plasmas: phase transitions, transport, quantum, and magnetic field effects,” Eur. Phys. J. D 72, 84 (2018)

    2018

  36. [44]

    Electronic density response of warm dense mat- ter,

    Tobias Dornheim, Zhandos A. Moldabekov, Kushal Ra- makrishna, Panagiotis Tolias, Andrew D. Baczewski, Dominik Kraus, Thomas R. Preston, David A. Chap- man, Maximilian P. B¨ ohme, Tilo D¨ oppner, Frank Graziani, Michael Bonitz, Attila Cangi, and Jan Vor- berger, “Electronic den...

    2023

  37. [45]

    Giuliani and G

    G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cam- bridge, 2008)

    2008

  38. [46]

    Anderson, Quantum Monte Carlo: Origins, Devel- opment, Applications (Oxford University Press, USA, 2007)

    J.B. Anderson, Quantum Monte Carlo: Origins, Devel- opment, Applications (Oxford University Press, USA, 2007)

    2007

  39. [47]

    On path integral Monte Carlo simulations,

    M. F. Herman, E. J. Bruskin, and B. J. Berne, “On path integral Monte Carlo simulations,” J. Chem. Phys. 76, 5150–5155 (1982)

    1982

  40. [48]

    Simulation of quan- tum many-body systems by path-integral methods,

    E. L. Pollock and D. M. Ceperley, “Simulation of quan- tum many-body systems by path-integral methods,” Phys. Rev. B 30, 2555–2568 (1984)

    1984

  41. [49]

    Monte Carlo Calculation of Quantum Systems,

    Minoru Takahashi and Masatoshi Imada, “Monte Carlo Calculation of Quantum Systems,” J. Phys. Soc. Jpn 53, 963–974 (1984)

    1984

  42. [50]

    The uniform electron gas at warm dense matter conditions,

    T. Dornheim, S. Groth, and M. Bonitz, “The uniform electron gas at warm dense matter conditions,” Phys. Rep. 744, 1–86 (2018)

    2018

  43. [51]

    The uniform electron gas,

    P.-F. Loos and P. M. W. Gill, “The uniform electron gas,” Comput. Mol. Sci 6, 410–429 (2016)

    2016

  44. [52]

    Ground state of the electron gas by a stochastic method,

    D. M. Ceperley and B. J. Alder, “Ground state of the electron gas by a stochastic method,” Phys. Rev. Lett. 45, 566–569 (1980)

    1980

  45. [53]

    Correlation energy, structure factor, radial distribution function, and momentum dis- tribution of the spin-polarized uniform electron gas,

    G. Ortiz and P. Ballone, “Correlation energy, structure factor, radial distribution function, and momentum dis- tribution of the spin-polarized uniform electron gas,” Phys. Rev. B 50, 1391–1405 (1994)

    1994

  46. [54]

    Zero temperature phases of the electron gas,

    G. Ortiz, M. Harris, and P. Ballone, “Zero temperature phases of the electron gas,” Phys. Rev. Lett. 82, 5317– 5320 (1999)

    1999

  47. [55]

    Static re- sponse from quantum Monte Carlo calculations,

    S. Moroni, D. M. Ceperley, and G. Senatore, “Static re- sponse from quantum Monte Carlo calculations,” Phys. Rev. Lett 69, 1837 (1992)

    1992

  48. [56]

    Static response and local field factor of the electron gas,

    S. Moroni, D. M. Ceperley, and G. Senatore, “Static response and local field factor of the electron gas,” Phys. Rev. Lett 75, 689 (1995)

    1995

  49. [57]

    Quantum Monte Carlo study of the three-dimensional 15 spin-polarized homogeneous electron gas,

    G. G. Spink, R. J. Needs, and N. D. Drummond, “Quantum Monte Carlo study of the three-dimensional 15 spin-polarized homogeneous electron gas,” Phys. Rev. B 88, 085121 (2013)

    2013

  50. [58]

    Density functional theory: Its origins, rise to prominence, and future,

    R. O. Jones, “Density functional theory: Its origins, rise to prominence, and future,” Rev. Mod. Phys. 87, 897– 923 (2015)

    2015

  51. [59]

    Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas,

    Ethan W. Brown, Bryan K. Clark, Jonathan L. DuBois, and David M. Ceperley, “Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas,” Phys. Rev. Lett. 110, 146405 (2013)

    2013

  52. [60]

    Ab initio thermodynamic results for the degenerate electron gas at finite temperature,

    T. Schoof, S. Groth, J. Vorberger, and M. Bonitz, “Ab initio thermodynamic results for the degenerate electron gas at finite temperature,” Phys. Rev. Lett.115, 130402 (2015)

    2015

  53. [61]

    Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature,

    V. S. Filinov, V. E. Fortov, M. Bonitz, and Zh. Mold- abekov, “Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature,” Phys. Rev. E 91, 033108 (2015)

    2015

  54. [62]

    Ab initio quan- tum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit,

    T. Dornheim, S. Groth, T. Sjostrom, F. D. Malone, W. M. C. Foulkes, and M. Bonitz, “Ab initio quan- tum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit,” Phys. Rev. Lett. 117, 156403 (2016)

    2016

  55. [63]

    Ab initio exchange– correlation free energy of the uniform electron gas at warm dense matter conditions,

    S. Groth, T. Dornheim, T. Sjostrom, F. D. Malone, W. M. C. Foulkes, and M. Bonitz, “Ab initio exchange– correlation free energy of the uniform electron gas at warm dense matter conditions,” Phys. Rev. Lett. 119, 135001 (2017)

    2017

  56. [64]

    Interaction picture density matrix quantum Monte Carlo,

    Fionn D. Malone, N. S. Blunt, James J. Shepherd, D. K. K. Lee, J. S. Spencer, and W. M. C. Foulkes, “Interaction picture density matrix quantum Monte Carlo,” J. Chem. Phys. 143, 044116 (2015)

    2015

  57. [65]

    Accurate exchange-correlation en- ergies for the warm dense electron gas,

    Fionn D. Malone, N. S. Blunt, Ethan W. Brown, D. K. K. Lee, J. S. Spencer, W. M. C. Foulkes, and James J. Shepherd, “Accurate exchange-correlation en- ergies for the warm dense electron gas,” Phys. Rev. Lett. 117, 115701 (2016)

    2016

  58. [66]

    Restricted configuration path integral Monte Carlo,

    A. Yilmaz, K. Hunger, T. Dornheim, S. Groth, and M. Bonitz, “Restricted configuration path integral Monte Carlo,” J. Chem. Phys. 153, 124114 (2020)

    2020

  59. [67]

    Exchange-correlation effect in the charge response of a warm dense electron gas,

    Peng-Cheng Hou, Bao-Zong Wang, Kristjan Haule, Youjin Deng, and Kun Chen, “Exchange-correlation effect in the charge response of a warm dense electron gas,” Phys. Rev. B 106, L081126 (2022)

    2022

  60. [68]

    A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite tem- peratures: Issues, observations, and benchmark study,

    Joonho Lee, Miguel A. Morales, and Fionn D. Mal- one, “A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite tem- peratures: Issues, observations, and benchmark study,” J. Chem. Phys. 154, 064109 (2021)

    2021

  61. [69]

    The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation,

    T. Dornheim, J. Vorberger, S. Groth, N. Hoffmann, Zh.A. Moldabekov, and M. Bonitz, “The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation,” J. Chem. Phys 151, 194104 (2019)

    2019

  62. [70]

    Configuration path integral Monte Carlo approach to the static density response of the warm dense electron gas,

    S. Groth, T. Dornheim, and M. Bonitz, “Configuration path integral Monte Carlo approach to the static density response of the warm dense electron gas,” J. Chem. Phys 147, 164108 (2017)

    2017

  63. [71]

    Strongly coupled electron liquid: Ab initio path integral Monte Carlo simulations and di- electric theories,

    Tobias Dornheim, Travis Sjostrom, Shigenori Tanaka, and Jan Vorberger, “Strongly coupled electron liquid: Ab initio path integral Monte Carlo simulations and di- electric theories,” Phys. Rev. B 101, 045129 (2020)

    2020

  64. [72]

    Effective static approximation: A fast and re- liable tool for warm-dense matter theory,

    Tobias Dornheim, Attila Cangi, Kushal Ramakrishna, Maximilian B¨ ohme, Shigenori Tanaka, and Jan Vor- berger, “Effective static approximation: A fast and re- liable tool for warm-dense matter theory,” Phys. Rev. Lett. 125, 235001 (2020)

    2020

  65. [73]

    Analytical representation of the local field correction of the uniform electron gas within the effec- tive static approximation,

    Tobias Dornheim, Zhandos A. Moldabekov, and Pana- giotis Tolias, “Analytical representation of the local field correction of the uniform electron gas within the effec- tive static approximation,” Phys. Rev. B 103, 165102 (2021)

    2021

  66. [74]

    Spin-resolved density response of the warm dense electron gas,

    Tobias Dornheim, Jan Vorberger, Zhandos A. Mold- abekov, and Panagiotis Tolias, “Spin-resolved density response of the warm dense electron gas,” Phys. Rev. Res. 4, 033018 (2022)

    2022

  67. [75]

    Nonlinear electronic density response in warm dense matter,

    Tobias Dornheim, Jan Vorberger, and Michael Bonitz, “Nonlinear electronic density response in warm dense matter,” Phys. Rev. Lett. 125, 085001 (2020)

    2020

  68. [76]

    Den- sity response of the warm dense electron gas beyond linear response theory: Excitation of harmonics,

    Tobias Dornheim, Maximilian B¨ ohme, Zhandos A. Moldabekov, Jan Vorberger, and Michael Bonitz, “Den- sity response of the warm dense electron gas beyond linear response theory: Excitation of harmonics,” Phys. Rev. Res. 3, 033231 (2021)

    2021

  69. [77]

    Nonlinear density response from imaginary- time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas,

    Tobias Dornheim, Zhandos A. Moldabekov, and Jan Vorberger, “Nonlinear density response from imaginary- time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas,” J. Chem. Phys. 155, 054110 (2021)

    2021

  70. [78]

    Nonlinear density response and higher order correlation functions in warm dense matter,

    Tobias Dornheim, Jan Vorberger, and Zhandos A. Moldabekov, “Nonlinear density response and higher order correlation functions in warm dense matter,” J. Phys. Soc. Jpn 90, 104002 (2021)

    2021

  71. [79]

    Ab initio results for the static structure factor of the warm dense electron gas,

    Tobias Dornheim, Simon Groth, and Michael Bonitz, “Ab initio results for the static structure factor of the warm dense electron gas,” Contrib. Plasma Phys. 57, 468–478 (2017)

    2017

  72. [80]

    Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results,

    Kai Hunger, Tim Schoof, Tobias Dornheim, Michael Bonitz, and Alexey Filinov, “Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results,” Phys. Rev. E 103, 053204 (2021)

    2021

  73. [81]

    Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature with- out fixed nodes,

    Tobias Dornheim, Maximilian B¨ ohme, Burkhard Mil- itzer, and Jan Vorberger, “Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature with- out fixed nodes,” Phys. Rev. B 103, 205142 (2021)

    2021

  74. [82]

    Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization,

    Tobias Dornheim, Jan Vorberger, Burkhard Militzer, and Zhandos A. Moldabekov, “Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization,” Phys. Rev. E 104, 055206 (2021)

    2021

  75. [83]

    Lowering of the kinetic energy in interacting quantum systems,

    Burkhard Militzer and E. L. Pollock, “Lowering of the kinetic energy in interacting quantum systems,” Phys. Rev. Lett. 89, 280401 (2002)

    2002

  76. [84]

    Path integral Monte Carlo calculation of the momentum dis- tribution of the homogeneous electron gas at finite tem- perature,

    B. Militzer, E.L. Pollock, and D.M. Ceperley, “Path integral Monte Carlo calculation of the momentum dis- tribution of the homogeneous electron gas at finite tem- perature,” High Energy Density Phys. 30, 13–20 (2019)

    2019

  77. [85]

    The uniform electron gas at high temperatures: ab initio path integral Monte Carlo simulations and analytical theory,

    Tobias Dornheim, Jan Vorberger, Zhandos Moldabekov, Gerd R¨ opke, and Wolf-Dietrich Kraeft, “The uniform electron gas at high temperatures: ab initio path integral Monte Carlo simulations and analytical theory,” High Energy Density Phys. 45, 101015 (2022)

    2022

  78. [86]

    Virial coefficients of the uniform electron gas from path-integral Monte Carlo simulations,

    G. R¨ opke, T. Dornheim, J. Vorberger, D. Blaschke, and B. Mahato, “Virial coefficients of the uniform electron gas from path-integral Monte Carlo simulations,” Phys. Rev. E 109, 025202 (2024)

    2024

  79. [87]

    Physical insights from imaginary-time density–density correla- tion functions,

    Tobias Dornheim, Zhandos Moldabekov, Panagiotis To- 16 lias, Maximilian B¨ ohme, and Jan Vorberger, “Physical insights from imaginary-time density–density correla- tion functions,” Matter Rad. Extrem. 8, 056601 (2023)

    2023

  80. [88]

    Analysing the dy- namic structure of warm dense matter in the imaginary- time domain: theoretical models and simulations,

    Tobias Dornheim, Jan Vorberger, Zhandos A. Mold- abekov, and Maximilian B¨ ohme, “Analysing the dy- namic structure of warm dense matter in the imaginary- time domain: theoretical models and simulations,” Phil. Trans. Roy. Soc A 381, 20220217 (2023)

    2023

  81. [89]

    Extraction of the frequency moments of spectral densities from imaginary-time correlation func- tion data,

    Tobias Dornheim, Damar C. Wicaksono, Juan E. Suarez-Cardona, Panagiotis Tolias, Maximilian P. B¨ ohme, Zhandos A. Moldabekov, Michael Hecht, and Jan Vorberger, “Extraction of the frequency moments of spectral densities from imaginary-time correlation func- tion data,” Phys. Re...

    2023

  82. [90]

    Ab initio path integral Monte Carlo results for the dy- namic structure factor of correlated electrons: From the electron liquid to warm dense matter,

    T. Dornheim, S. Groth, J. Vorberger, and M. Bonitz, “Ab initio path integral Monte Carlo results for the dy- namic structure factor of correlated electrons: From the electron liquid to warm dense matter,” Phys. Rev. Lett. 121, 255001 (2018)

    2018

  83. [91]

    Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas,

    S. Groth, T. Dornheim, and J. Vorberger, “Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas,” Phys. Rev. B 99, 235122 (2019)

    2019

  84. [92]

    Electronic pair alignment and roton feature in the warm dense electron gas,

    Tobias Dornheim, Zhandos Moldabekov, Jan Vorberger, Hanno K¨ ahlert, and Michael Bonitz, “Electronic pair alignment and roton feature in the warm dense electron gas,” Communications Physics 5, 304 (2022)

    2022

  85. [93]

    A. V. Filinov, J. Ara, and I. M. Tkachenko, “Dynami- cal response in strongly coupled uniform electron liq- uids: Observation of plasmon-roton coexistence using nine sum rules, Shannon information entropy, and path- integral Monte Carlo simulations,” Phys. Rev. B 107, 195143 (2023)

    2023

  86. [94]

    Fourier–Matsubara series expansion for imaginary–time correlation functions,

    Panagiotis Tolias, Fotios Kalkavouras, and Tobias Dornheim, “Fourier–Matsubara series expansion for imaginary–time correlation functions,” J. Chem. Phys. 160, 181102 (2024)

    2024

  87. [95]

    Dynamic exchange correlation effects in the strongly coupled electron liquid,

    Tobias Dornheim, Panagiotis Tolias, Fotios Kalka- vouras, Zhandos A. Moldabekov, and Jan Vorberger, “Dynamic exchange correlation effects in the strongly coupled electron liquid,” Phys. Rev. B 110, 075137 (2024)

    2024

  88. [96]

    Quantum delocalization, structural order, and density response of the strongly coupled electron liquid,

    Tobias Dornheim, Panagiotis Tolias, Jan Vorberger, and Zhandos A. Moldabekov, “Quantum delocalization, structural order, and density response of the strongly coupled electron liquid,” Europhys. Lett. 147, 36001 (2024)

    2024

  89. [97]

    Short wavelength limit of the dynamic Matsubara local field correction,

    Tobias Dornheim, Panagiotis Tolias, Zhandos Mold- abekov, and Jan Vorberger, “Short wavelength limit of the dynamic Matsubara local field correction,” (2024), arXiv:2408.04669 [cond-mat.str-el]

    2024 arXiv

  90. [98]

    Accurate homogeneous electron gas exchange-correlation free energy for local spin-density calculations,

    Valentin V. Karasiev, Travis Sjostrom, James Dufty, and S. B. Trickey, “Accurate homogeneous electron gas exchange-correlation free energy for local spin-density calculations,” Phys. Rev. Lett. 112, 076403 (2014)

    2014

  91. [99]

    Sta- tus of free-energy representations for the homogeneous electron gas,

    V. V. Karasiev, S. B. Trickey, and J. W. Dufty, “Sta- tus of free-energy representations for the homogeneous electron gas,” Phys. Rev. B 99, 195134 (2019)

    2019

  92. [100]

    Thermal properties of the inhomo- geneous electron gas,

    N. David Mermin, “Thermal properties of the inhomo- geneous electron gas,” Phys. Rev. 137, A1441–A1443 (1965)

    1965

  93. [101]

    Im- portance of finite-temperature exchange correlation for warm dense matter calculations,

    V. V. Karasiev, L. Calderin, and S. B. Trickey, “Im- portance of finite-temperature exchange correlation for warm dense matter calculations,” Phys. Rev. E 93, 063207 (2016)

    2016

  94. [102]

    Gradient cor- rections to the exchange-correlation free energy,

    Travis Sjostrom and J´ erˆ ome Daligault, “Gradient cor- rections to the exchange-correlation free energy,” Phys. Rev. B 90, 155109 (2014)

    2014

  95. [103]

    Influence of finite temperature exchange- correlation effects in hydrogen,

    Kushal Ramakrishna, Tobias Dornheim, and Jan Vorberger, “Influence of finite temperature exchange- correlation effects in hydrogen,” Phys. Rev. B 101, 195129 (2020)

    2020

  96. [104]

    Nonempirical semilocal free-energy density functional for matter under extreme conditions,

    Valentin V. Karasiev, James W. Dufty, and S. B. Trickey, “Nonempirical semilocal free-energy density functional for matter under extreme conditions,” Phys. Rev. Lett. 120, 076401 (2018)

    2018

  97. [105]

    Meta-gga exchange-correlation free energy density functional to increase the accuracy of warm dense mat- ter simulations,

    Valentin V. Karasiev, D. I. Mihaylov, and S. X. Hu, “Meta-gga exchange-correlation free energy density functional to increase the accuracy of warm dense mat- ter simulations,” Phys. Rev. B 105, L081109 (2022)

    2022

  98. [106]

    Generalized gradient approximation made thermal,

    John Kozlowski, Dennis Perchak, and Kieron Burke, “Generalized gradient approximation made thermal,” (2023), arXiv:2308.03319

    2023 arXiv

  99. [107]

    Statistical physics of dense plasmas: Thermo- dynamics, transport coefficients and dynamic correla- tions,

    Setsuo Ichimaru, Hiroshi Iyetomi, and Shigenori Tanaka, “Statistical physics of dense plasmas: Thermo- dynamics, transport coefficients and dynamic correla- tions,” Phys. Rep. 149, 91–205 (1987)

    1987

  100. [108]

    Direct free energy calcu- lation from ab initio path integral Monte Carlo simula- tions of warm dense matter,

    Tobias Dornheim, Zhandos Moldabekov, Sebastian Schwalbe, and Jan Vorberger, “Direct free energy calcu- lation from ab initio path integral Monte Carlo simula- tions of warm dense matter,” (2024), arXiv:2407.01044 [cond-mat.quant-gas]

    2024 arXiv

  101. [109]

    Krauth, Statistical Mechanics: Algorithms and Computations, Oxford Master Series in Physics (Oxford University Press, UK, 2006)

    W. Krauth, Statistical Mechanics: Algorithms and Computations, Oxford Master Series in Physics (Oxford University Press, UK, 2006)

    2006

  102. [110]

    Theory of noninteracting fermions and bosons in the canonical ensemble,

    Hatem Barghathi, Jiangyong Yu, and Adrian Del Mae- stro, “Theory of noninteracting fermions and bosons in the canonical ensemble,” Phys. Rev. Res. 2, 043206 (2020)

    2020

  103. [111]

    Canonical parti- tion functions: ideal quantum gases, interacting classical gases, and interacting quantum gases,

    Chi-Chun Zhou and Wu-Sheng Dai, “Canonical parti- tion functions: ideal quantum gases, interacting classical gases, and interacting quantum gases,” J. Stat. Mech. 2018, 023105 (2018)

    2018

  104. [112]

    η-ensemble path integral monte carlo approach to the free energy of the warm dense electron gas and the uniform electron liquid,

    Tobias Dornheim, Panagiotis Tolias, Zhandos Mold- abekov, and Jan Vorberger, “ η-ensemble path integral monte carlo approach to the free energy of the warm dense electron gas and the uniform electron liquid,” (2024), arXiv:2412.13596 [physics.chem-ph]

    2024 arXiv

  105. [113]

    Binding energy, microstructure, and shell model of Coulomb clusters,

    Kenji Tsuruta and Setsuo Ichimaru, “Binding energy, microstructure, and shell model of Coulomb clusters,” Phys. Rev. A 48, 1339–1344 (1993)

    1993

  106. [114]

    Structure of spherical three-dimensional Coulomb crystals,

    P. Ludwig, S. Kosse, and M. Bonitz, “Structure of spherical three-dimensional Coulomb crystals,” Phys. Rev. E 71, 046403 (2005)

    2005

  107. [115]

    Complex plas- mas: a laboratory for strong correlations,

    M. Bonitz, C. Henning, and D. Block, “Complex plas- mas: a laboratory for strong correlations,” Rep. Prog. Phys. 73, 066501 (2010)

    2010

  108. [116]

    Trapped non- neutral plasmas, liquids, and crystals (the thermal equi- librium states),

    Daniel H. E. Dubin and T. M. O’Neil, “Trapped non- neutral plasmas, liquids, and crystals (the thermal equi- librium states),” Rev. Mod. Phys. 71, 87–172 (1999)

    1999

  109. [117]

    Electrons in artificial atoms,

    R. C. Ashoori, “Electrons in artificial atoms,” Nature 379, 413–419 (1996)

    1996

  110. [118]

    Or- dering and phase transitions of charged particles in a classical finite two-dimensional system,

    Vladimir M. Bedanov and Franc ¸ ois M. Peeters, “Or- dering and phase transitions of charged particles in a classical finite two-dimensional system,” Phys. Rev. B 49, 2667–2676 (1994)

    1994

  111. [119]

    Efficient estimation of free energy dif- ferences from Monte Carlo data,

    C. H. Bennet, “Efficient estimation of free energy dif- ferences from Monte Carlo data,” J. Comput. Phys. 22, 17 245 (1976)

    1976

  112. [120]

    Quantitative com- parison and optimization of methods for evaluating the chemical potential by molecular simulation,

    D. A. Kofke and Cummings P. T., “Quantitative com- parison and optimization of methods for evaluating the chemical potential by molecular simulation,” Mol. Phys. 92, 973 (1997)

    1997

  113. [121]

    Simulation of the chemical potential and the cavity free energy of dense hard-sphere fluids,

    Phil Attard, “Simulation of the chemical potential and the cavity free energy of dense hard-sphere fluids,” J. Chem. Phys. 98, 2225 (1993)

    1993

  114. [122]

    The chemical potential in dense fluids and fluid mixtures via computer simula- tion,

    Shing K. S. and Gubbins K. E., “The chemical potential in dense fluids and fluid mixtures via computer simula- tion,” Mol. Phys. 46, 1109 (1982)

    1982

  115. [123]

    Spatially resolved thermodynamic inte- gration: An efficient method to compute chemical po- tentials of dense fluids,

    M. Heidari, K. Kremer, R. Cortes-Huerto, and R. Potestio, “Spatially resolved thermodynamic inte- gration: An efficient method to compute chemical po- tentials of dense fluids,” J. Chem. Theory Comput. 14, 3409 (2018)

    2018

  116. [124]

    High-Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases,

    R. W. Zwanzig, “High-Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases,” J. Chem. Phys. 22, 1420 (1954)

    1954

  117. [125]

    Potential-distribution theory and the sta- tistical mechanics of fluids,

    B. Widom, “Potential-distribution theory and the sta- tistical mechanics of fluids,” J. Phys. Chem. 86, 869 (1982)

    1982

  118. [126]

    Widom inser- tion method in simulations with Ewald summation,

    Amin Bakhshandeh and Yan Levin, “Widom inser- tion method in simulations with Ewald summation,” J. Chem. Phys. 156, 134110 (2022)

    2022

  119. [127]

    Quantum monte carlo measurement of the chemical potential of 4He,

    C. M. Herdman, A. Rommal, and A. Del Maestro, “Quantum monte carlo measurement of the chemical potential of 4He,” Phys. Rev. B 89, 224502 (2014)

    2014

  120. [128]

    Finite- size corrections to the chemical potential,

    J I Siepmann, I R McDonald, and D Frenkel, “Finite- size corrections to the chemical potential,” J. Phys. Con- dens. Matter 4, 679 (1992)

    1992

  121. [129]

    Finite-size error in many-body simulations with long-range interactions,

    Simone Chiesa, David M. Ceperley, Richard M. Martin, and Markus Holzmann, “Finite-size error in many-body simulations with long-range interactions,” Phys. Rev. Lett. 97, 076404 (2006)

    2006

  122. [130]

    Finite-size errors in continuum quantum Monte Carlo calculations,

    N. D. Drummond, R. J. Needs, A. Sorouri, and W. M. C. Foulkes, “Finite-size errors in continuum quantum Monte Carlo calculations,” Phys. Rev. B 78, 125106 (2008)

    2008

  123. [131]

    Overcoming finite-size effects in electronic structure simulations at extreme conditions,

    Tobias Dornheim and Jan Vorberger, “Overcoming finite-size effects in electronic structure simulations at extreme conditions,” J. Chem. Phys. 154, 144103 (2021)

    2021

  124. [132]

    Finite-size corrections for a number of observables haven been implemented into the UEGPY package, see https://github.com/fdmalone/uegpy

  125. [133]

    Theory of finite size effects for elec- tronic quantum Monte Carlo calculations of liquids and solids,

    Markus Holzmann, Raymond C. Clay, Miguel A. Morales, Norm M. Tubman, David M. Ceperley, and Carlo Pierleoni, “Theory of finite size effects for elec- tronic quantum Monte Carlo calculations of liquids and solids,” Phys. Rev. B 94, 035126 (2016)

    2016

  126. [134]

    Equation of state of partially ionized hydrogen and deuterium plasma revis- ited,

    A. V. Filinov and M. Bonitz, “Equation of state of partially ionized hydrogen and deuterium plasma revis- ited,” Phys. Rev. E 108, 055212 (2023)

    2023

  127. [135]

    Ab initio path integral Monte Carlo simulations of warm dense two-component systems without fixed nodes: Structural properties,

    Tobias Dornheim, Sebastian Schwalbe, Maximilian P. B¨ ohme, Zhandos A. Moldabekov, Jan Vorberger, and Panagiotis Tolias, “Ab initio path integral Monte Carlo simulations of warm dense two-component systems without fixed nodes: Structural properties,” J. Chem. Phys. 160, 164111 (2024)

    2024

  128. [136]

    Static Electronic Den- sity Response of Warm Dense Hydrogen: Ab Initio Path Integral Monte Carlo Simulations,

    Maximilian B¨ ohme, Zhandos A. Moldabekov, Jan Vor- berger, and Tobias Dornheim, “Static Electronic Den- sity Response of Warm Dense Hydrogen: Ab Initio Path Integral Monte Carlo Simulations,” Phys. Rev. Lett. 129, 066402 (2022)

    2022

  129. [137]

    Path integral Monte Carlo simulation of the low-density hydrogen plasma,

    B. Militzer and D. M. Ceperley, “Path integral Monte Carlo simulation of the low-density hydrogen plasma,” Phys. Rev. E 63, 066404 (2001)

    2001

  130. [138]

    First- principles equation of state database for warm dense matter computation,

    Burkhard Militzer, Felipe Gonz´ alez-Cataldo, Shuai Zhang, Kevin P. Driver, and Fran ¸ cois Soubiran, “First- principles equation of state database for warm dense matter computation,” Phys. Rev. E 103, 013203 (2021)

    2021

  131. [139]

    Path integrals in the theory of con- densed helium,

    D. M. Ceperley, “Path integrals in the theory of con- densed helium,” Rev. Mod. Phys 67, 279 (1995)

    1995

  132. [140]

    Worm algorithm for continuous-space path integral Monte Carlo simulations,

    M. Boninsegni, N. V. Prokofev, and B. V. Svistunov, “Worm algorithm for continuous-space path integral Monte Carlo simulations,” Phys. Rev. Lett 96, 070601 (2006)

    2006

  133. [141]

    Path integral Monte Carlo simulation of degener- ate electrons: Permutation-cycle properties,

    T. Dornheim, S. Groth, A. V. Filinov, and M. Bonitz, “Path integral Monte Carlo simulation of degener- ate electrons: Permutation-cycle properties,” J. Chem. Phys. 151, 014108 (2019)

    2019

  134. [142]

    Fermion sign problem in path inte- gral Monte Carlo simulations: Quantum dots, ultracold atoms, and warm dense matter,

    T. Dornheim, “Fermion sign problem in path inte- gral Monte Carlo simulations: Quantum dots, ultracold atoms, and warm dense matter,” Phys. Rev. E 100, 023307 (2019)

    2019

  135. [143]

    Finite- size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with peri- odic boundary conditions,

    Louisa M. Fraser, W. M. C. Foulkes, G. Rajagopal, R. J. Needs, S. D. Kenny, and A. J. Williamson, “Finite- size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with peri- odic boundary conditions,” Phys. Rev. B 53, 1814–1832 (1996)

    1996

  136. [144]

    Hansen and I.R

    J.P. Hansen and I.R. McDonald, Theory of simple liq- uids : with applications to soft matter(Academic Press, 2013)

    2013

  137. [145]

    Fermion sign problem in path inte- gral Monte Carlo simulations: grand-canonical ensem- ble,

    Tobias Dornheim, “Fermion sign problem in path inte- gral Monte Carlo simulations: grand-canonical ensem- ble,” J. Phys. A - Math. Theor. 54, 335001 (2021)

    2021

  138. [146]

    Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations,

    M. Boninsegni, N. V. Prokofev, and B. V. Svistunov, “Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations,” Phys. Rev. E 74, 036701 (2006)

    2006

  139. [147]

    Computational complex- ity and fundamental limitations to fermionic quantum Monte Carlo simulations,

    M. Troyer and U. J. Wiese, “Computational complex- ity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett 94, 170201 (2005)

    2005

  140. [148]

    ISHTAR - Imaginary-time Stochastic High- performance Tool for Ab initio Research,

    Tobias Dornheim, Maximilian B¨ ohme, and Sebastian Schwalbe, “ISHTAR - Imaginary-time Stochastic High- performance Tool for Ab initio Research,” (2024)

    2024

  141. [149]

    High order Chin actions in path integral Monte Carlo,

    K. Sakkos, J. Casulleras, and J. Boronat, “High order Chin actions in path integral Monte Carlo,” J. Chem. Phys. 130, 204109 (2009)

    2009

  142. [150]

    High-order path-integral Monte Carlo methods for solving quantum dot problems,

    Siu A. Chin, “High-order path-integral Monte Carlo methods for solving quantum dot problems,” Phys. Rev. E 91, 031301 (2015)

    2015

  143. [151]

    Permutation blocking path integral Monte Carlo: a highly efficient approach to the simu- lation of strongly degenerate non-ideal fermions,

    Tobias Dornheim, Simon Groth, Alexey Filinov, and Michael Bonitz, “Permutation blocking path integral Monte Carlo: a highly efficient approach to the simu- lation of strongly degenerate non-ideal fermions,” New J. Phys. 17, 073017 (2015)

    2015

  144. [152]

    Fermion nodes,

    D. M. Ceperley, “Fermion nodes,” J. Stat. Phys. 63, 1237–1267 (1991)

    1991

  145. [153]

    Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integra- tion,

    Tobias Dornheim, Michele Invernizzi, Jan Vorberger, and Barak Hirshberg, “Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integra- tion,” J. Chem. Phys. 153, 234104 (2020)

    2020

  146. [154]

    Ab 18 initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes,

    S. Groth, T. Schoof, T. Dornheim, and M. Bonitz, “Ab 18 initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes,” Phys. Rev. B 93, 085102 (2016)

    2016

  147. [155]

    Fast, Hierarchical, and Adap- tive Algorithm for Metropolis Monte Carlo Simulations of Long-Range Interacting Systems,

    Fabio M¨ uller, Henrik Christiansen, Stefan Schnabel, and Wolfhard Janke, “Fast, Hierarchical, and Adap- tive Algorithm for Metropolis Monte Carlo Simulations of Long-Range Interacting Systems,” Phys. Rev. X 13, 031006 (2023)

    2023

  148. [156]

    Quantum ring-polymer con- traction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics,

    Christopher John, Thomas Spura, Scott Habershon, and Thomas D. K¨ uhne, “Quantum ring-polymer con- traction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics,” Phys. Rev. E 93, 043305 (2016)

    2016

  149. [157]

    On the thermody- namic properties of fictitious identical particles and the application to fermion sign problem,

    Yunuo Xiong and Hongwei Xiong, “On the thermody- namic properties of fictitious identical particles and the application to fermion sign problem,” J. Chem. Phys. 157, 094112 (2022)

    2022

  150. [158]

    Fermionic physics from ab initio path inte- gral Monte Carlo simulations of fictitious identical par- ticles,

    Tobias Dornheim, Panagiotis Tolias, Simon Groth, Zhandos A. Moldabekov, Jan Vorberger, and Barak Hirshberg, “Fermionic physics from ab initio path inte- gral Monte Carlo simulations of fictitious identical par- ticles,” J. Chem. Phys. 159, 164113 (2023)

    2023

  151. [159]

    Ab initio path integral Monte Carlo simulations of the uniform electron gas on large length scales,

    Tobias Dornheim, Sebastian Schwalbe, Zhandos A. Moldabekov, Jan Vorberger, and Panagiotis Tolias, “Ab initio path integral Monte Carlo simulations of the uniform electron gas on large length scales,” J. Phys. Chem. Lett. 15, 1305–1313 (2024)

    2024

  152. [160]

    Inte- gral equation theory based dielectric scheme for strongly coupled electron liquids,

    P. Tolias, F. Lucco Castello, and T. Dornheim, “Inte- gral equation theory based dielectric scheme for strongly coupled electron liquids,” J. Chem. Phys. 155, 134115 (2021)

    2021

  153. [161]

    Quantum version of the integral equation theory-based dielectric scheme for strongly coupled elec- tron liquids,

    Panagiotis Tolias, Federico Lucco Castello, and Tobias Dornheim, “Quantum version of the integral equation theory-based dielectric scheme for strongly coupled elec- tron liquids,” J. Chem. Phys. 158, 141102 (2023)

    2023

  154. [162]

    Clas- sical bridge functions in classical and quantum plasma liquids,

    F. Lucco Castello, P. Tolias, and T. Dornheim, “Clas- sical bridge functions in classical and quantum plasma liquids,” Europhys. Lett. 138, 44003 (2022)

    2022

  155. [163]

    Reproducibility in density functional the- ory calculations of solids,

    Kurt Lejaeghere, Gustav Bihlmayer, Torbj¨ orn Bj¨ orkman, Peter Blaha, Stefan Bl¨ ugel, Volker Blum, Damien Caliste, Ivano E. Castelli, Stewart J. Clark, Andrea Dal Corso, Stefano de Gironcoli, Thierry Deutsch, John Kay Dewhurst, Igor Di Marco, Clau- dia Draxl, Marcin Du lak, ...

    2016

  156. [164]

    Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements,

    G Kresse and J Hafner, “Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements,” Journal of Physics: Condensed Matter 6, 8245 (1994)

    1994

  157. [165]

    Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,

    David Vanderbilt, “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,” Phys. Rev. B41, 7892–7895 (1990)

    1990

  158. [166]

    Attard, Thermodynamics and Statistical Mechanics: Equilibrium by Entropy Maximisation(Academic Press, 2002)

    P. Attard, Thermodynamics and Statistical Mechanics: Equilibrium by Entropy Maximisation(Academic Press, 2002)

    2002

  159. [167]

    Widom, Statistical mechanics: A concise introduc- tion for chemists(Cambridge University Press, 2002)

    B. Widom, Statistical mechanics: A concise introduc- tion for chemists(Cambridge University Press, 2002)

    2002

  160. [168]

    Consistency conditions for the integral equations of liquid structures,

    E. Lomba and L. L. Lee, “Consistency conditions for the integral equations of liquid structures,” Int. J. Thermo- phys. 17, 663 (1996)

    1996

  161. [169]

    Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid,

    Panagiotis Tolias, Federico Lucco Castello, Fotios Kalkavouras, and Tobias Dornheim, “Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid,” Phys. Rev. B 109, 125134 (2024)

    2024

  162. [170]

    Balescu, Equilibrium and nonequilibrium statistical mechanics (John Wiley & Sons, 1975)

    R. Balescu, Equilibrium and nonequilibrium statistical mechanics (John Wiley & Sons, 1975)

    1975

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.