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arxiv: 2606.24615 · v1 · pith:D262R35Cnew · submitted 2026-06-23 · 🪐 quant-ph · cond-mat.mes-hall· cond-mat.quant-gas· cond-mat.stat-mech

Quantum-enabled active matter at the atomic scale

Sabrina Burgardt , Julian Fe{\ss} , Alexander Guthmann , Silvia Hiebel , Aritra K. Mukhopadhyay , Sangyun Lee , Michael te Vrugt , Benno Liebchen
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Hartmut L\"owen Raphael Wittkowski Artur Widera
This is my paper

Pith reviewed 2026-06-25 23:46 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hallcond-mat.quant-gascond-mat.stat-mech
keywords active matterultracold atomsquantum spin exchangeoptical dipole trapCs-133Rb-87active Langevin modelMonte Carlo simulations
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The pith

Individual cesium atoms extract energy from a rubidium bath via quantum spin exchange and convert it into active motion.

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

The paper shows that single Cs-133 atoms held in an optical dipole trap can pull energy out of an ultracold Rb-87 bath through quantum spin interactions and turn that energy into directed kinetic motion. A model built from kinetic theory reproduces the observed trajectories with no adjustable parameters, and Monte Carlo simulations confirm that the energy transfer occurs in discrete spin-exchange events. This places active-matter behavior at the scale of individual atoms, where quantum mechanics governs the energy-conversion step. A sympathetic reader would care because it supplies a concrete, testable route to study how internal quantum degrees of freedom can drive non-equilibrium motion at the smallest sizes.

Core claim

Individual Cs-133 atoms confined in an optical dipole trap extract energy from an ultracold bath of Rb-87 atoms via quantum-mechanical spin interactions and convert it into active motion. The resulting dynamics are quantitatively reproduced by a parameter-free active Langevin model derived from kinetic theory, supported by event-driven Monte Carlo collision simulations. The microscopic origin of the activity is identified as quantum spin exchange, which transfers discrete internal spin energy into kinetic motion.

What carries the argument

Quantum spin exchange between individual Cs and Rb atoms, which converts discrete internal spin energy into center-of-mass kinetic motion.

If this is right

  • Active matter exists at the single-atom scale with quantum mechanics as the energy-conversion mechanism.
  • A parameter-free Langevin description derived from kinetic theory suffices to predict the trajectories.
  • Quantum spin exchange supplies a microscopic channel that links internal-state energy to external motion.
  • The setup opens quantitative study of mesoscopic non-equilibrium thermodynamics driven by discrete quantum events.

Where Pith is reading between the lines

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

  • Controlling the initial spin populations could allow engineered trajectories or directed transport without external fields.
  • The same spin-exchange mechanism might be tested in other atomic pairs or in optical lattices to vary dimensionality.
  • Time-resolved spin-state measurements correlated with velocity changes would directly map energy quanta to motion quanta.

Load-bearing premise

The observed atomic motion arises specifically from quantum spin exchange rather than other heating or scattering channels.

What would settle it

Prepare the atoms in hyperfine states that forbid spin exchange and check whether the active motion disappears while other scattering channels remain open.

Figures

Figures reproduced from arXiv: 2606.24615 by Alexander Guthmann, Aritra K. Mukhopadhyay, Artur Widera, Benno Liebchen, Hartmut L\"owen, Julian Fe{\ss}, Michael te Vrugt, Raphael Wittkowski, Sabrina Burgardt, Sangyun Lee, Silvia Hiebel.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: c shows an exemplary evolution of the density distribution at a fixed magnetic field of B = 2 G. The width sz,Cs first steeply increases to reach a peak value [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: a shows that increasing the magnetic field – and thus the activation energy Q – leads to a progres￾sively stronger modification of the Cs density distribu￾tion. We find that the width sz,Cs of an active Cs ensem￾ble can exceed that of a passive one by nearly a factor of four at the largest magnetic field applied, B = 3 G, cor￾responding to an activation energy of Q = kB × 110 TRb. This indicates that activ… view at source ↗
Figure 4
Figure 4. Figure 4: shows that the modification of the Cs density distribution becomes weaker at higher Rb cloud temper￾atures. This is because the collision energies are compa￾rably high at higher temperatures, reducing the relative impact of the activation energy Q on the active motion. For instance, the width sz,Cs of active Cs atoms in a Rb cloud with TRb = 1075(10) nK exceeds that of passive Cs atoms only by a factor of … view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
read the original abstract

Active matter comprises particles that extract energy from their local environment and convert it into motion. Although active particles have been miniaturized down to the nanoscale, realizing activity at the fundamentally smaller scale of individual atoms remains an open challenge, where quantum effects become increasingly relevant. Here, we experimentally demonstrate that individual Cs-133 atoms confined in an optical dipole trap extract energy from an ultracold bath of Rb-87 atoms via quantum-mechanical spin interactions and convert it into active motion. We quantitatively reproduce the resulting dynamics using a parameter-free active Langevin model derived from kinetic theory and support it with event-driven Monte Carlo collision simulations. The microscopic origin of activity is identified as quantum spin exchange, which transfers discrete internal spin energy into kinetic motion. Our work establishes a quantum-enabled route to active matter at the fundamental size limit of single atoms and opens perspectives for exploring the interplay of activity, quantum physics, and mesoscopic non-equilibrium thermodynamics.

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

2 major / 1 minor

Summary. The manuscript claims to experimentally demonstrate that individual Cs-133 atoms in an optical dipole trap extract energy from an ultracold Rb-87 bath via quantum-mechanical spin interactions and convert it into active motion. The resulting dynamics are quantitatively reproduced by a parameter-free active Langevin model derived from kinetic theory and supported by event-driven Monte Carlo collision simulations. The microscopic origin of the activity is identified as quantum spin exchange transferring discrete internal spin energy into kinetic motion.

Significance. If the central claims hold, the work would establish a quantum-enabled route to active matter at the single-atom scale and open perspectives on the interplay between activity, quantum physics, and mesoscopic non-equilibrium thermodynamics. The parameter-free derivation from kinetic theory and the use of Monte Carlo simulations would constitute notable strengths if the zero-parameter status and quantitative match to data are explicitly verified.

major comments (2)
  1. [Abstract] Abstract: the claim of quantitative agreement with a 'parameter-free' active Langevin model is presented without any figures, error bars, data-selection criteria, or explicit verification that the model contains zero fitted parameters; this prevents confirmation that the prediction does not implicitly depend on quantities fitted to the same experiment.
  2. [Abstract] Abstract/Results: no controls are described to isolate quantum spin exchange as the dominant driver (e.g., varying hyperfine states, magnetic fields, or laser detunings to suppress vs. enable exchange while holding other scattering rates fixed). Alternative channels such as residual photon scattering or elastic momentum transfer could produce similar kinetics, leaving the microscopic identification unsecured.
minor comments (1)
  1. [Abstract] Abstract: the Monte Carlo simulations are cited as support but without explicit comparison metrics or statements showing that only the spin-exchange term reproduces the measured statistics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of quantitative agreement with a 'parameter-free' active Langevin model is presented without any figures, error bars, data-selection criteria, or explicit verification that the model contains zero fitted parameters; this prevents confirmation that the prediction does not implicitly depend on quantities fitted to the same experiment.

    Authors: The abstract is a concise summary and does not include figures or detailed verification, which is standard. The full manuscript (Section III, Figs. 2-4, and Methods) derives the active Langevin model from kinetic theory with explicitly zero fitted parameters; all inputs are taken from independent measurements or literature values. Error bars, data-selection criteria, and the quantitative match are shown in the main text. We will revise the abstract to reference this verification explicitly. revision: partial

  2. Referee: [Abstract] Abstract/Results: no controls are described to isolate quantum spin exchange as the dominant driver (e.g., varying hyperfine states, magnetic fields, or laser detunings to suppress vs. enable exchange while holding other scattering rates fixed). Alternative channels such as residual photon scattering or elastic momentum transfer could produce similar kinetics, leaving the microscopic identification unsecured.

    Authors: The identification rests on the observed energy transfer precisely matching the Rb hyperfine splitting (not elastic momentum transfer) and on Monte Carlo simulations reproducing the data only when the spin-exchange channel is included. We will add a discussion paragraph in the revised manuscript explicitly ruling out alternative channels using the existing quantitative match and simulation results. Explicit experimental controls of the suggested type were not performed. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an experimental demonstration of Cs atoms gaining active motion from a Rb bath via spin exchange, supported by a parameter-free active Langevin model derived from kinetic theory and Monte Carlo simulations. No load-bearing derivation step reduces by construction to a fitted input, self-citation chain, or self-definitional loop; the model is explicitly positioned as independently derived from external kinetic theory without adjustable parameters fitted to the target data. The identification of spin exchange as the microscopic driver rests on experimental controls and simulation comparisons rather than tautological renaming or imported uniqueness theorems. This is the normal case of a self-contained experimental claim with external theoretical grounding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of kinetic theory to spin-exchange collisions in the ultracold regime and on the experimental isolation of spin-exchange as the sole energy-transfer channel; no free parameters are claimed and no new entities are introduced.

axioms (1)
  • domain assumption Kinetic theory accurately describes the spin-exchange collision rates between Cs and Rb in the ultracold regime
    Invoked to derive the active Langevin equation without adjustable constants

pith-pipeline@v0.9.1-grok · 5738 in / 1166 out tokens · 31963 ms · 2026-06-25T23:46:10.463402+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

71 extracted references · 2 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    In the first step, we perform an all-optical preparation of the thermal Rb cloud

    Experimental sequence and observables The initial preparation of the two atomic samples is carried out sequentially in spatially separated regions. In the first step, we perform an all-optical preparation of the thermal Rb cloud. This stage consists of a laser-cooling step followed by evaporative cooling in an anisotropic, crossed optical dipole trap (ODT...

  2. [2]

    We choose a right-hand coordinate system which is oriented in such a way that gravity acts along thex-direction

    Optical dipole trap model The ODT potential of our experiment is generated by two crossed laser beams at a wavelength of 1064 nm. We choose a right-hand coordinate system which is oriented in such a way that gravity acts along thex-direction. One laser beam is traveling along thez-direction and the second one is traveling along thex-direction. We employ a...

  3. [3]

    Importantly, the Cs-Cs interaction is negligible due to the extremely low Cs density

    Scattering properties In our experiment, the atoms interact via ultracold two-body collisions, with both Rb-Rb and Rb-Cs interactions being repulsive. Importantly, the Cs-Cs interaction is negligible due to the extremely low Cs density. We quantify 12 0 10 20el (10 11 cm2) Q a 0 50 100se (10 11 cm2) Q b 10 3 100 103 Ec/kB ( K) 0 20 40el (10 11 cm3/s) Q 10...

  4. [4]

    The heating is accompanied by a constant loss of Rb atoms from the ODT

    Rb lifetime We find that the Rb cloud is constantly heated during the interaction with the Cs atoms. The heating is accompanied by a constant loss of Rb atoms from the ODT. Possible heating sources are recombination heating due to three-body recombination, technical noise, or spontaneous scattering of trap photons [61–63]. We detect the atom numberN Rb an...

    1929

  5. [5]

    Event-driven Monte-Carlo collision simulations We use numerical event-driven Monte-Carlo collision simulations to model the active motion of individual Cs atoms inside the Rb cloud. The Rb cloud is modeled as a thermalized, classical gas with a time-dependent temperature and density, i.e., the heating of the Rb cloud in the ODT is included, but the dynami...

  6. [6]

    (3) for an ensemble ofN Cs = 5000 Cs atoms

    Langevin simulations To validate our model, we performed three-dimensional (3D) stochastic numerical simulations of Eq. (3) for an ensemble ofN Cs = 5000 Cs atoms. We initialized the Cs atoms by sampling their positions and velocities from a Maxwell-Boltzmann distribution at initial temperatureT Cs,0 = 2.4µK; the initial spatial widthss j,Cs (j∈ {x, y, z}...

  7. [7]

    M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrody- namics of soft active matter, Rev. Mod. Phys.85, 1143 (2013)

    2013

  8. [8]

    Bechinger, R

    C. Bechinger, R. Di Leonardo, H. L¨ owen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys.88, 045006 (2016)

    2016

  9. [9]

    Cavagna and I

    A. Cavagna and I. Giardina, Bird flocks as condensed matter, Annu. Rev. Condens. Matter Phys.5, 183 (2014)

    2014

  10. [10]

    I. S. Aranson, Bacterial active matter, Rep. Progr. Phys. 85, 076601 (2022)

    2022

  11. [11]

    Doostmohammadi, J

    A. Doostmohammadi, J. Ign´ es-Mullol, J. M. Yeomans, and F. Sagu´ es, Active nematics, Nat. Commun.9, 3246 (2018)

    2018

  12. [12]

    Z. Shi, Z. Zhang, J. Schnermann, S. C. Neuhauss, N. Nama, R. Wittkowski, and D. Ahmed, Ultrasound- driven programmable artificial muscles, Nature646, 1096 (2025)

    2025

  13. [13]

    F. C. Landers, L. Hertle, V. Pustovalov, D. Sivakumaran, C. M. Oral, O. Brinkmann, K. Meiners, P. Theiler, V. Gantenbein, A. Veciana, M. Mattmann, S. Riss, S. Gervasoni, C. Chautems, H. Ye, S. Sevim, A. D. Flouris, J. Puigmart´ ı-Luis, T. Sotto Mayor, P. Alves, T. L¨ uhmann, X. Chen, N. Ochsenbein, U. Moehrlen, T. Schubert, Z. Kulcsar, P. Gruber, M. Weiss...

    2025

  14. [14]

    Walther and A

    A. Walther and A. H. E. M¨ uller, Janus particles, Soft Matter4, 663 (2008)

    2008

  15. [15]

    S. Chen, D. E. Fan, P. Fischer, A. Ghosh, K. G¨ opfrich, R. Golestanian, H. Hess, X. Ma, B. J. Nelson, T. Pati˜ no Padial, J. Tang, K. Villa, W. Wang, L. Zhang, A. Sen, and S. S´ anchez, A roadmap for next-generation nanomotors, Nat. Nanotech.20, 990 (2025)

    2025

  16. [16]

    Calero, E

    C. Calero, E. L. Sibert III, and R. Rey, Self- thermophoresis at the nanoscale using light induced sol- vation dynamics, Nanoscale12, 7557 (2020)

    2020

  17. [17]

    S. M. Douglas, I. Bachelet, and G. M. Church, A logic- gated nanorobot for targeted transport of molecular pay- loads, Science335, 831 (2012)

    2012

  18. [18]

    Ciuti, R

    G. Ciuti, R. J. Webster III, K.-W. Kwok, and A. Menci- assi, Robotic surgery, Nat. Rev. Bioeng.3, 565 (2025)

    2025

  19. [19]

    Y. Amir, E. Ben-Ishay, D. Levner, S. Ittah, A. Abu- Horowitz, and I. Bachelet, Universal computing by DNA origami robots in a living animal, Nat. Nanotech.9, 353 (2014)

    2014

  20. [20]

    K. Wang, W. Chen, B. Guo, Q. Huang, G. Zhu, H. Ni, L. Zhang, M. Perez, R. Sha, N. C. Seeman, and P. M. Chaikin, A tunable autonomous RNA-fueled micro- engine, Nat. Commun.17, 3164 (2026)

    2026

  21. [21]

    Adachi, K

    K. Adachi, K. Takasan, and K. Kawaguchi, Activity- induced phase transition in a quantum many-body sys- tem, Phys. Rev. Res.4, 013194 (2022)

    2022

  22. [22]

    Takasan, K

    K. Takasan, K. Adachi, and K. Kawaguchi, Activity- induced ferromagnetism in one-dimensional quantum many-body systems, Phys. Rev. Res.6, 023096 (2024)

    2024

  23. [23]

    Khasseh, S

    R. Khasseh, S. Wald, R. Moessner, C. A. Weber, and M. Heyl, Active quantum flocks, Phys. Rev. Lett.135, 248302 (2025)

    2025

  24. [24]

    Yamagishi, N

    M. Yamagishi, N. Hatano, and H. Obuse, Proposal of a quantum version of active particles via a nonunitary quantum walk, Sci. Rep.14, 28648 (2024)

    2024

  25. [25]

    Penner, L

    A.-G. Penner, L. Viotti, R. Fazio, L. Arrachea, and F. von Oppen, Heat-to-motion conversion for quantum active matter, Phys. Rev. B112, L180303 (2025)

    2025

  26. [26]

    J. F. Steiner, F. von Oppen, and R. Egger, Active quantum matter from monitored pure-state dynamics, arXiv:2603.12629 10.48550/arXiv.2603.12629 (2026)

    work page doi:10.48550/arxiv.2603.12629 2026

  27. [27]

    A. P. Antonov, Y. Zheng, B. Liebchen, and H. L¨ owen, Engineering active motion in quantum matter, Phys. Rev. Res.7, 033008 (2025)

    2025

  28. [28]

    A. P. Antonov, S. Lee, B. Liebchen, H. L¨ owen, J. Melles, G. Morigi, Y. Tuchkov, and M. te Vrugt, Modeling dis- sipation in quantum active matter, Phys. Rev. A (ac- cepted) (2026)

    2026

  29. [29]

    Hanai, D

    R. Hanai, D. Ootsuki, and R. Tazai, Photoinduced non- reciprocal magnetism, Nat. Commun.16, 8195 (2025)

    2025

  30. [30]

    Nadolny, C

    T. Nadolny, C. Bruder, and M. Brunelli, Nonreciprocal synchronization of active quantum spins, Phys. Rev. X 15, 011010 (2025)

    2025

  31. [31]

    Rieser, M

    J. Rieser, M. A. Ciampini, H. Rudolph, N. Kiesel, K. Hornberger, B. A. Stickler, M. Aspelmeyer, and U. Deli´ c, Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles, Science377, 987 (2022)

    2022

  32. [32]

    Reisenbauer, H

    M. Reisenbauer, H. Rudolph, L. Egyed, K. Hornberger, A. V. Zasedatelev, M. Abuzarli, B. A. Stickler, and U. Deli´ c, Non-Hermitian dynamics and non-reciprocity of optically coupled nanoparticles, Nat. Phys.20, 1629 (2024)

    2024

  33. [33]

    G. V. Kolmakov and I. S. Aranson, Superfluid swimmers, Phys. Rev. Res.3, 013188 (2021)

    2021

  34. [34]

    Baker-Rasooli, T

    M. Baker-Rasooli, T. Aladjidi, T. D. Ferreira, A. Bra- mati, M. Albert, P.-E. Larr´ e, and Q. Glorieux, Swimming against a superfluid flow: Self-propulsion via vortex- antivortex shedding in a quantum fluid of light, Phys. Rev. Lett.136, 223401 (2026)

    2026

  35. [35]

    Massignan, S

    P. Massignan, S. Richard, G. E. Astrakharchik, A. ˙Imamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, Polarons in atomic gases and two-dimensional semicon- ductors, Rev. Mod. Phys. (accepted) (2026)

    2026

  36. [36]

    Gross and W

    C. Gross and W. Bakr, Quantum gas microscopy for sin- gle atom and spin detection, Nat. Phys.17, 1316 (2021)

    2021

  37. [37]

    Grusdt, N

    F. Grusdt, N. Mostaan, E. Demler, and L. A. P. Ardila, Impurities and polarons in bosonic quantum gases: a re- view on recent progress, Rep. Prog. Phys.88, 066401 (2025)

    2025

  38. [38]

    Baroni, G

    C. Baroni, G. Lamporesi, and M. Zaccanti, Quantum mixtures of ultracold gases of neutral atoms, Nat. Rev. Phys.6, 736 (2024)

    2024

  39. [39]

    L.-N. Wu, J. Nettersheim, J. Feß, A. Schnell, S. Burgardt, S. Hiebel, D. Adam, A. Eckardt, and A. Widera, Indica- tion of critical scaling in time during the relaxation of an open quantum system, Nat. Commun.15, 1714 (2024)

    2024

  40. [40]

    Schmidt, D

    F. Schmidt, D. Mayer, Q. Bouton, D. Adam, T. Lausch, N. Spethmann, and A. Widera, Quantum spin dy- namics of individual neutral impurities coupled to a Bose-Einstein condensate, Phys. Rev. Lett.121, 130403 (2018)

    2018

  41. [41]

    Schmidt, D

    F. Schmidt, D. Mayer, Q. Bouton, D. Adam, T. Lausch, 23 J. Nettersheim, E. Tiemann, and A. Widera, Tailored single-atom collisions at ultralow energies, Phys. Rev. Lett.122, 013401 (2019)

    2019

  42. [42]

    Le Blay, J

    M. Le Blay, J. H. K. Saldi, and A. Morin, Control of collective activity to crystallize an oscillator gas, Nat. Phys.21, 1412 (2025)

    2025

  43. [43]

    S. A. M. Loos and S. H. L. Klapp, Irreversibility, heat and information flows induced by non-reciprocal interactions, New. J. Phys.22, 123051 (2020)

    2020

  44. [44]

    Nardini, ´E

    C. Nardini, ´E. Fodor, E. Tjhung, F. van Wijland, J. Tailleur, and M. E. Cates, Entropy production in field theories without time-reversal symmetry: quantify- ing the non-equilibrium character of active matter, Phys. Rev. X7, 021007 (2017)

    2017

  45. [45]

    Thomas, M

    R. Thomas, M. Chilcott, C. Chisholm, A. B. Deb, M. Horvath, B. J. Sawyer, and N. Kjærgaard, Quantum scattering in an optical collider for ultracold atoms, J. Phys.: Conf. Ser.875, 012007 (2017)

    2017

  46. [46]

    M. S. J. Horvath, R. Thomas, E. Tiesinga, A. B. Deb, and N. Kjærgaard, Above-threshold scattering about a feshbach resonance for ultracold atoms in an optical col- lider, Nat. Commun.8, 452 (2017)

    2017

  47. [47]

    E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, Interisotope determination of ultracold rubidium interactions from three high-precision experiments, Phys. Rev. Lett.88, 093201 (2002)

    2002

  48. [48]

    Fiasconaro, E

    A. Fiasconaro, E. Gudowska-Nowak, and W. Ebeling, Tuning active Brownian motion with shot-noise energy pulses, J. Stat. Mech.2009, P01029 (2009)

    2009

  49. [49]

    Di Bello, R

    C. Di Bello, R. Majumdar, R. Marathe, R. Metzler, and ´E. Rold´ an, Brownian particle in a Poisson-shot-noise ac- tive bath: exact statistics, effective temperature, and in- ference, Ann. Phys. (Berlin)536, 2300427 (2024)

    2024

  50. [50]

    Ferrari, A proper mobility formula for large, heavy particles in gases in any regime, Chem

    L. Ferrari, A proper mobility formula for large, heavy particles in gases in any regime, Chem. Phys.257, 63 (2000)

    2000

  51. [51]

    Ferrari, Particles dispersed in a dilute gas: Limits of validity of the Langevin equation, Chem

    L. Ferrari, Particles dispersed in a dilute gas: Limits of validity of the Langevin equation, Chem. Phys.336, 27 (2007)

    2007

  52. [52]

    Dunkel and P

    J. Dunkel and P. H¨ anggi, Relativistic Brownian mo- tion: From a microscopic binary collision model to the Langevin equation, Phys. Rev. E74, 051106 (2006)

    2006

  53. [53]

    Hohmann, F

    M. Hohmann, F. Kindermann, T. Lausch, D. Mayer, F. Schmidt, E. Lutz, and A. Widera, Individual tracer atoms in an ultracold dilute gas, Phys. Rev. Lett.118, 263401 (2017)

    2017

  54. [54]

    Lin and P

    H. Lin and P. Danielewicz, One-body Langevin dynam- ics in heavy-ion collisions at intermediate energies, Phys. Rev. C99, 024612 (2019)

    2019

  55. [55]

    Londo˜ no, J

    M. Londo˜ no, J. Madro˜ nero, and J. P´ erez-R´ ıos, Dynam- ics of a single trapped ion in a high-density medium: A stochastic approach, Phys. Rev. A106, 022803 (2022)

    2022

  56. [56]

    Londo˜ no, J

    M. Londo˜ no, J. Madro˜ nero, and J. P´ erez-R´ ıos, Cold atom-ion systems in radio-frequency multipole traps: Event-driven molecular dynamics and stochastic simu- lations, Phys. Rev. A108, 053324 (2023)

    2023

  57. [57]

    A. A. Dubkov, P. H¨ anggi, and I. Goychuk, Non-linear Brownian motion: The problem of obtaining the ther- mal Langevin equation for a non-Gaussian bath, J. Stat. Mech.2009, P01034 (2009)

    2009

  58. [58]

    Barbosa, M

    S. Barbosa, M. Miefer-Emmanouilidis, F. Lang, J. Koch, and A. Widera, Stabilizing an ultracold fermi gas against fermi acceleration to superdiffusion through localization, Phys. Rev. Lett.134, 253402 (2025)

    2025

  59. [59]

    Finelli, B

    S. Finelli, B. Restivo, A. Ciamei, A. Trenkwalder, M. In- guscio, D. Petrov, S. Skipetroc, and M. Zaccanti, Anoma- lous diffusion and localization in a disorder-free atomic mixture, arXiv:2601.13226 (2026)

    arXiv 2026

  60. [60]

    Y. Sagi, M. Brook, I. Almog, and N. Davidson, Observa- tion of anomalous diffusion and fractional self-similarity in one dimension, Phys. Rev. Lett.108, 093002 (2012)

    2012

  61. [61]

    G. Afek, J. Coslovsky, A. Courvoisier, O. Livneh, and N. Davidson, Observing power-law dynamics of position- velocity correlation in anomalous diffusion, Phys. Rev. Lett.119, 060602 (2017)

    2017

  62. [62]

    Paparelle, J

    I. Paparelle, J. Henaff, J. Garcia-Beni, E. Gillet, D. Mon- tesinos, G. L. Giorgi, M. C. Soriano, R. Zambrini, and V. Parigi, Experimental memory control in continuous- variable optical quantum reservoir computing, Nat. Pho- ton.20, 413 (2026)

    2026

  63. [63]

    Jeggle and R

    J. Jeggle and R. Wittkowski, Intelligent matter consist- ing of active particles, inArtificial Intelligence and In- telligent Matter, edited by M. te Vrugt (Springer, Cham, Switzerland, 2026) pp. 273–288

    2026

  64. [64]

    Gaimann and M

    M. Gaimann and M. Klopotek, Optimal information in- jection and transfer mechanisms for active matter reser- voir computing, arXiv:2509.01799 (2025)

    arXiv 2025

  65. [65]

    Cannoni, Relativisticσv rel in the calculation of relics abundances: A closer look, Phys

    M. Cannoni, Relativisticσv rel in the calculation of relics abundances: A closer look, Phys. Rev. D89, 103533 (2014)

    2014

  66. [66]

    J. M. Hutson, Feshbach resonances in ultracold atomic and molecular collisions: threshold behaviour and sup- pression of poles in scattering lengths, New J. Phys.9, 152 (2007)

    2007

  67. [67]

    Weber, J

    T. Weber, J. Herbig, M. Mark, H.-C. N¨ agerl, and R. Grimm, Three-body recombination at large scatter- ing lengths in an ultracold atomic gas, Phys. Rev. Lett. 91, 123201 (2003)

    2003

  68. [68]

    M. E. Gehm, K. M. O’Hara, T. A. Savard, and J. E. Thomas, Dynamics of noise-induced heating in atom traps, Phys. Rev. A58, 3914 (1998)

    1998

  69. [69]

    Optical dipole traps for neutral atoms

    R. Grimm, M. Weidem¨ uller, and Y. B. Ovchin- nikov, Optical dipole traps for neutral atoms, arXiv:physics/9902072 10.48550/arXiv.physics/9902072 (1999)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.physics/9902072 1999

  70. [70]

    C. Kim, E. K. Lee, P. H¨ anggi, and P. Talkner, Numerical method for solving stochastic differential equations with Poissonian white shot noise, Phys. Rev. E76, 011109 (2007)

    2007

  71. [71]

    Rossani and G

    A. Rossani and G. Spiga, Kinetic theory with inelastic in- teractions, Transp. Theory Statist. Phys.27, 273 (1998)

    1998