Comptes Rendus
Energy-space random walk in a driven disordered Bose gas
Comptes Rendus. Physique, Online first (2023), pp. 1-19.

Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, Et η with η=0.46(2), and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schrödinger-equation simulations reveal a crossover from η0.5 to η0.4 with increasing disorder strength, hinting at the existence of two different dynamical regimes. We present a semi-classical model that captures the simulation results and allows an understanding of the dynamics in terms of an energy-space random walk, from which a crossover from Et 1/2 to Et 2/5 scaling is analytically obtained. The two limits correspond to the random walk being limited by the rate of the elastic disorder-induced scattering or the rate at which the drive can change the system’s energy. Our results provide the theoretical foundation for further experiments.

Motivés par l’observation expérimentale [1] que le forçage d’un gaz de bosons sans interaction dans une boîte 3D en présence d’un faible désordre conduit à une croissance de l’énergie en loi de puissance, Et η avec η=0,46(2), et à des distributions en impulsion exponentielles comprimées révélant une loi d’échelle dynamique sous-jacente, nous effectuons des études numériques et analytiques systématiques de ce système. Des simulations de l’équation de Schrödinger montrent un passage de η0,5 à η0,4 lorsqu’on augmente la force du désordre, ce qui laisse supposer l’existence de deux régimes dynamiques différents. Nous présentons un modèle semi-classique qui rend compte des résultats des simulations et permet de comprendre la dynamique en termes de marche aléatoire dans l’espace des énergies, grâce à quoi un passage de la loi d’échelle Et 1/2 à la loi Et 2/5 est obtenu analytiquement. Les deux lois limites correspondent au fait que la marche aléatoire est limitée par le taux de la diffusion élastique induite par le désordre ou au contraire par le taux avec lequel le forçage peut modifier l’énergie du système. Nos résultats fournissent une base théorique aux futures études expérimentales.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/crphys.168
Keywords: Ultracold atoms, Disordered system, Dynamic scaling, Continuous-time random walk, Chaos
Mot clés : Atomes froids, Système désordonné, Loi d’échelle dynamique, Marche aléatoire en temps continu, Chaos

Yansheng Zhang 1; Gevorg Martirosyan 1; Christopher Junhong Ho 1; Jiří Etrych 1; Christoph Eigen 1; Zoran Hadzibabic 1

1 Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Energy-space random walk in a driven disordered {Bose} gas},
     journal = {Comptes Rendus. Physique},
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     year = {2023},
     doi = {10.5802/crphys.168},
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Yansheng Zhang; Gevorg Martirosyan; Christopher Junhong Ho; Jiří Etrych; Christoph Eigen; Zoran Hadzibabic. Energy-space random walk in a driven disordered Bose gas. Comptes Rendus. Physique, Online first (2023), pp. 1-19. doi : 10.5802/crphys.168.

[1] G. Martirosyan; C. J. Ho; J. Etrych; Y. Zhang; A. Cao; Z. Hadzibabic; C. Eigen Observation of subdiffusive dynamic scaling in a driven and disordered Bose gas, 2023 (preprint) | arXiv

[2] M. Kardar Statistical Physics of Fields, Cambridge University Press, Cambridge, 2007 | DOI

[3] T. Nakayama; K. Yakubo; R. L. Orbach Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations, Rev. Mod. Phys., Volume 66 (1994), pp. 381-443 | DOI

[4] T. Halpin-Healy; Y.-C. Zhang Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics, Phys. Rep., Volume 254 (1995), pp. 215-414 | DOI

[5] G. Ódor Universality classes in nonequilibrium lattice systems, Rev. Mod. Phys., Volume 76 (2004), pp. 663-724 | DOI | MR | Zbl

[6] A. Polkovnikov; K. Sengupta; A. Silva; M. Vengalattore Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys., Volume 83 (2011), pp. 863-883 | DOI

[7] U. C. Täuber Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior, Cambridge University Press, Cambridge, 2014 | DOI

[8] E. Altman; R. Vosk Universal dynamics and renormalization in many-body-localized systems, Annu. Rev. Condens. Matter Phys., Volume 6 (2015) no. 1, pp. 383-409 | DOI

[9] T. Langen; R. Geiger; J. Schmiedmayer Ultracold atoms out of equilibrium, Annu. Rev. Condens. Matter Phys., Volume 6 (2015) no. 1, pp. 201-217 | DOI

[10] M. A. Muñoz Colloquium: Criticality and dynamical scaling in living systems, Rev. Mod. Phys., Volume 90 (2018), 031001 | DOI | MR

[11] A. N. Mikheev; I. Siovitz; T. Gasenzer Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium, 2023 (preprint) | arXiv

[12] Y. Sagi; M. Brook; I. Almog; N. Davidson Observation of anomalous diffusion and fractional self-similarity in one dimension, Phys. Rev. Lett., Volume 108 (2012), 093002 | DOI

[13] C.-L. Hung; V. Gurarie; C. Chin From cosmology to cold atoms: Observation of Sakharov oscillations in a quenched atomic superfluid, Science, Volume 341 (2013) no. 6151, pp. 1213-1215 | DOI

[14] P. Makotyn; C. E. Klauss; D. L. Goldberger; E. A. Cornell; D. S. Jin Universal dynamics of a degenerate unitary Bose gas, Nat. Phys., Volume 10 (2014), pp. 116-119 | DOI

[15] N. Navon; A. L. Gaunt; R. P. Smith; Z. Hadzibabic Emergence of a turbulent cascade in a quantum gas, Nature, Volume 539 (2016), pp. 72-75 | DOI

[16] M. Prüfer; P. Kunkel; H. Strobel; S. Lannig; D. Linnemann; C.-M. Schmied; J. Berges; T. Gasenzer; M. K. Oberthaler Observation of universal dynamics in a spinor Bose gas far from equilibrium, Nature, Volume 563 (2018) no. 7730, pp. 217-220 | DOI

[17] C. Eigen; J. A. P. Glidden; R. Lopes; E. A. Cornell; R. P. Smith; Z. Hadzibabic Universal prethermal dynamics of Bose gases quenched to unitarity, Nature, Volume 563 (2018) no. 7730, pp. 221-224 | DOI

[18] S. Erne; R. Bücker; T. Gasenzer; J. Berges; J. Schmiedmayer Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium, Nature, Volume 563 (2018) no. 7730, pp. 225-229 | DOI

[19] S. P. Johnstone; A. J. Groszek; P. T. Starkey; C. J. Billington; T. P. Simula; K. Helmerson Evolution of large-scale flow from turbulence in a two-dimensional superfluid, Science, Volume 364 (2019) no. 6447, pp. 1267-1271 | DOI | MR | Zbl

[20] R. Saint-Jalm; P. C. M. Castilho; E. Le Cerf; B. Bakkali-Hassani; J.-L. Ville; S. Nascimbene; J. Beugnon; J. Dalibard Dynamical symmetry and breathers in a two-dimensional Bose gas, Phys. Rev. X, Volume 9 (2019), 021035 | DOI

[21] J. A. P. Glidden; C. Eigen; L. H. Dogra; T. A. Hilker; R. P. Smith; Z. Hadzibabic Bidirectional dynamic scaling in an isolated Bose gas far from equilibrium, Nat. Phys., Volume 17 (2021) no. 4, pp. 457-461 | DOI

[22] M. Gałka; P. Christodoulou; M. Gazo; A. Karailiev; N. Dogra; J. Schmitt; Z. Hadzibabic Emergence of isotropy and dynamic scaling in 2D wave turbulence in a homogeneous Bose gas, Phys. Rev. Lett., Volume 129 (2022), 190402 | DOI

[23] D. Wei; A. Rubio-Abadal; B. Ye; F. Machado; J. Kemp; K. Srakaew; S. Hollerith; J. Rui; S. Gopalakrishnan; N. Y. Yao; I. Bloch; J. Zeiher Quantum gas microscopy of Kardar–Parisi–Zhang superdiffusion, Science, Volume 376 (2022) no. 6594, pp. 716-720 | DOI

[24] Y. Le; Y. Zhang; S. Gopalakrishnan; M. Rigol; D. S. Weiss Observation of hydrodynamization and local prethermalization in 1D Bose gases, Nature, Volume 618 (2023), pp. 494-499 | DOI

[25] S. Huh; K. Mukherjee; K. Kwon; J. Seo; S. I. Mistakidis; H. R. Sadeghpour; J.-Y. Choi Classifying the universal coarsening dynamics of a quenched ferromagnetic condensate, 2023 (preprint) | arXiv

[26] N. Navon; C. Eigen; J. Zhang; R. Lopes; A. L. Gaunt; K. Fujimoto; M. Tsubota; R. P. Smith; Z. Hadzibabic Synthetic dissipation and cascade fluxes in a turbulent quantum gas, Science, Volume 366 (2019) no. 6463, pp. 382-385 | DOI

[27] C. Jarzynski; W. J. Swiatecki A universal asymptotic velocity distribution for independent particles in a time-dependent irregular container, Nucl. Phys. A, Volume 552 (1993) no. 1, pp. 1-9 | DOI

[28] C. Jarzynski Energy diffusion in a chaotic adiabatic billiard gas, Phys. Rev. E, Volume 48 (1993), pp. 4340-4350 | DOI | MR

[29] G. Bunin; L. D’Alessio; Y. Kafri; A. Polkovnikov Universal energy fluctuations in thermally isolated driven systems, Nat. Phys., Volume 7 (2011) no. 11, pp. 913-917 | DOI

[30] W. Hodson; C. Jarzynski Energy diffusion and absorption in chaotic systems with rapid periodic driving, Phys. Rev. Res., Volume 3 (2021), 013219 | DOI

[31] W. Hodson; C. Jarzynski Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving, Phys. Rev. E, Volume 104 (2021), 064210 | DOI | MR

[32] L. E. Reichl; W. A. Lin Exact quantum model of field-induced resonance overlap, Phys. Rev. A, Volume 33 (1986), pp. 3598-3601 | DOI

[33] W. A. Lin; L. E. Reichl Spectral analysis of quantum-resonance zones, quantum Kolmogorov-Arnold-Moser theorem, and quantum-resonance overlap, Phys. Rev. A, Volume 37 (1988), pp. 3972-3985 | DOI

[34] C. Gardiner Handbook of Stochastic Methods, Springer, Heidelberg, 1985

[35] J. Klafter; I. M. Sokolov First Steps in Random Walks: From Tools to Applications, Oxford University Press, Oxford, 2011 | DOI

[36] K. S. Fa; E. K. Lenzi Power law diffusion coefficient and anomalous diffusion: Analysis of solutions and first passage time, Phys. Rev. E, Volume 67 (2003), 061105 | DOI

[37] 50 Years of Anderson Localization (E. Abrahams, ed.), World Scientific, Singapore, 2010 | DOI

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