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arxiv: 2605.17069 · v1 · pith:5TTGC3H5new · submitted 2026-05-16 · ❄️ cond-mat.other

Dynamic Many-Body Theory: The dynamics of atomic impurities in ⁴He

Eckhard Krotscheck This is my paper

Pith reviewed 2026-05-20 15:14 UTC · model grok-4.3

classification ❄️ cond-mat.other
keywords dynamic many-body theoryatomic impuritiessuperfluid heliumeffective massdispersion relationsmuoniumroton minimum
0
0 comments X

The pith

Making all correlation functions time-dependent derives the impurity self-energy in ^4He and yields effective masses matching experiment.

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

The paper extends static many-body calculations to the dynamics of atomic impurities in liquid ^4He by making correlation functions explicitly time-dependent. This produces a working formula for the impurity self-energy that incorporates the main physical effects, motivated by possible muonium experiments testing the universality of free fall. Effective masses calculated for ^3He and hydrogen impurities agree with existing measurements. Dispersion relations for muonic ^4He and antiprotonic ^4He are found to pass below the roton minimum of the host liquid. A reader would care because the approach supplies concrete, microscopic predictions for how light and exotic atoms move through a quantum fluid.

Core claim

By making all correlation functions time-dependent in direct analogy to the background liquid derivation, a working formula for the impurity self-energy is obtained that includes the most relevant physical effects. This leads to effective masses of ^3He and hydrogen atoms that agree well with available experiments. The dispersion relations of muonic ^4He and antiprotonic ^4He pass under the roton minimum. Muonium is estimated to have a chemical potential of about 19 meV while antiprotonic ^4He has a negative chemical potential.

What carries the argument

Time-dependent extension of correlation functions to derive the impurity self-energy.

If this is right

  • Effective masses of ^3He and hydrogen in ^4He follow directly from the time-dependent self-energy and match experiment.
  • Dispersion relations for muonic ^4He and antiprotonic ^4He lie below the roton minimum.
  • Muonium probes short-range atomic interactions because of its large zero-point motion and has a positive chemical potential near 19 meV.
  • Antiprotonic ^4He has a negative chemical potential.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same time-dependent method could be applied to other light impurities or different quantum host liquids.
  • Predicted muonium properties offer a concrete target for experiments that test the equivalence principle with unstable neutral atoms.
  • Passage under the roton minimum implies a specific coupling strength between the impurity and host-liquid excitations.

Load-bearing premise

Deriving the impurity self-energy by making all correlation functions time-dependent in direct analogy to the background liquid derivation captures the most relevant physical effects without missing important corrections.

What would settle it

A new measurement of the effective mass of hydrogen atoms in ^4He that deviates from the calculated value, or a dispersion curve for muonic ^4He that does not pass under the roton minimum.

Figures

Figures reproduced from arXiv: 2605.17069 by Eckhard Krotscheck.

Figure 1
Figure 1. Figure 1: FIG. 1. (color online) The figure shows the Aziz interaction [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: 15 [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (color online) The left figure shows the chemical pote [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (color online) The figure shows [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (color online) The figures show the individual contri [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (color online) The left figure shows the volume excess [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 –hω (meV) k (Å-1) eZS(k) 3He  p 4He µ 4He T D H Mu Kinematcs of impurity atoms in 4He FIG. 6. (color online) The figure shows the calculated phonon-roton spectrum from Ref. 17 (crosses) and the single particle spectra for the impurity atoms considered in this work as indicated in the legend. We stress that the notion that damping occurs at the… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (color online) The figure shows the calculated effectiv [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (color online) The left figure shows the dispersion re [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (color online) The figure shows at a density of [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (color online) The figures shows color maps of the ima [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
read the original abstract

We implement manifestly microscopic many-body methods to study the dynamics of atomic impurities in a host quantum fluid, specifically $^4$He. Our investigations are motivated by experiments of muonium atoms within $^4$He with the goal of testing the universality of free fall by neutral bound states using unstable particles. Structure calculations are performed using standard semi-analytic methods; we extend here the calculations of our previos work (Journal of Low Temperature Physics {\bf 93}, 415-449 (1993)) to muonic \he4, antiprotonic \he4 and mounium atoms within \he4. We find that the muonium impurity probes, due to its large zero-point motion, the atomic interaction at rather short distances. Its chemical potential is estimated to be about 19 meV. Antiprotonic \he4 has, on the other hand, a negative chemical potential. Dynamics is treated by making all correlation functions time-dependent. In analogy to the derivation of the dynamics of the background liquid, we derive a working formula for the impurity self-energy that includes the most relevant physical effects. Results for the effective mass of \he3 and hydrogen atoms agree well with available experiments. The dispersion relations of muonic \he4 and antiprotonic \he4 pass through under the roton minimum.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript develops a microscopic many-body theory for the dynamics of atomic impurities in superfluid ^4He. It extends prior static structure calculations (referencing the authors' 1993 JLTP work) to muonic ^4He, antiprotonic ^4He, and muonium by making all correlation functions time-dependent. A working formula for the impurity self-energy is derived in direct analogy to the background liquid dynamics. The paper reports that effective masses for ^3He and hydrogen impurities agree with available experiments, while the dispersion relations for muonic and antiprotonic ^4He pass under the roton minimum. The study is motivated by potential tests of free-fall universality with muonium.

Significance. If the central results hold, the work supplies a parameter-free microscopic framework for impurity dynamics in quantum liquids, extending variational many-body methods without introducing new adjustable parameters. This is a notable strength. Partial validation comes from agreement with experiment for ^3He and H effective masses, but the predictions for exotic impurities (large zero-point motion, negative chemical potential) would have broader impact for guiding precision experiments if the analogy captures all relevant effects.

major comments (1)
  1. [Derivation of impurity self-energy] In the derivation of the impurity self-energy (obtained 'in analogy to the derivation of the dynamics of the background liquid' as described in the abstract and methods), the manuscript does not explicitly specify the form of the formula or address whether additional terms are needed to account for the impurity's distinct mass, zero-point motion, or local density response. This assumption is load-bearing for the reported dispersion relations of muonic ^4He and antiprotonic ^4He passing under the roton minimum, as the paper itself highlights the large zero-point motion for muonium; omitted corrections could alter the effective mass and dispersion results.
minor comments (3)
  1. [Abstract] Typo in abstract: 'previos' should be 'previous'.
  2. [Abstract] Spelling in abstract: 'mounium' should be 'muonium'.
  3. [Abstract] The phrasing 'pass through under the roton minimum' is unclear; rephrase to 'lie below the roton minimum' or provide a precise definition of what this means for the dispersion curve.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comment below and have revised the manuscript to improve clarity on the derivation.

read point-by-point responses

  1. Referee: In the derivation of the impurity self-energy (obtained 'in analogy to the derivation of the dynamics of the background liquid' as described in the abstract and methods), the manuscript does not explicitly specify the form of the formula or address whether additional terms are needed to account for the impurity's distinct mass, zero-point motion, or local density response. This assumption is load-bearing for the reported dispersion relations of muonic ^4He and antiprotonic ^4He passing under the roton minimum, as the paper itself highlights the large zero-point motion for muonium; omitted corrections could alter the effective mass and dispersion results.

    Authors: We thank the referee for this observation. The impurity self-energy is derived in Section 3 by extending the time-dependent variational method used for the pure liquid, with all correlation functions promoted to time dependence. The working formula incorporates the impurity mass directly in the kinetic-energy term of the variational functional and captures zero-point motion through the optimized time-dependent impurity-host correlations, which adjust to the impurity's lighter mass and greater delocalization. The host's local density response enters via its dynamic structure factor. No additional correction terms are required because the approach remains fully microscopic and parameter-free. To remove any ambiguity, we have added the explicit self-energy expression and a short justification of these points in the revised manuscript. This clarification supports the reported dispersion results without altering them. revision: yes

Circularity Check

0 steps flagged

Derivation applies established method to new system without reducing outputs to inputs by construction

full rationale

The paper extends prior structure calculations by making correlation functions time-dependent and derives the impurity self-energy formula in analogy to the background liquid case. This constitutes an application of the same microscopic variational framework to a distinct physical problem (atomic impurities with different masses and interactions), rather than a redefinition or refitting of the target quantities. Results for effective masses of ^3He and H are compared to independent external experiments, while dispersions for muonic and antiprotonic ^4He are presented as predictions. No equation is shown to equal its input by construction, no load-bearing premise rests solely on an unverified self-citation chain, and the central claims remain falsifiable against external data. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the time-dependent many-body framework transferred from the pure liquid to the impurity case; no explicit free parameters or new entities are named in the abstract.

axioms (1)
  • domain assumption Making correlation functions time-dependent in direct analogy to the background liquid captures the dominant dynamical effects for the impurity.
    Invoked when deriving the working formula for the impurity self-energy.

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Reference graph

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