Quantum diffusion and thermalization at resonant tunneling

Parra-Murillo, Carlos A.; Madroñero, Javier; Wimberger, Sandro

doi:10.1103/physreva.89.053610

Cited by 19 publications

(22 citation statements)

References 42 publications

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“…Moreover, the panels (a-c) in Fig. 4 confirm the expectation of most chaoticity in the region around U/J ≈ 1 at average atom numbers per site of order one [5][6][7][8][9][10][11].…”

Section: Spectral Analysissupporting

confidence: 73%

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Spectral analysis of two-dimensional Bose-Hubbard models

Fischer¹,

Hoffmann²,

Wimberger³

2016

Phys. Rev. A

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One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple twodimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest neighbor couplings at each site.

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“…Moreover, the panels (a-c) in Fig. 4 confirm the expectation of most chaoticity in the region around U/J ≈ 1 at average atom numbers per site of order one [5][6][7][8][9][10][11].…”

Section: Spectral Analysissupporting

confidence: 73%

“…Later extended models were also investigated, see e.g. [7][8][9][10][11], which essentially confirmed these results. Recently, a semiclassical theory has been developed to understand the chaotic behavior of one-dimensional BHMs and to put the results mentioned above onto a firmer ground [12].…”

Section: Introductionsupporting

confidence: 64%

Spectral analysis of two-dimensional Bose-Hubbard models

Fischer¹,

Hoffmann²,

Wimberger³

2016

Phys. Rev. A

Self Cite

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“…Also a semiclassical Gutzwiller trace formula is brought forward [177] for the Bose-Hubbard model in the chaotic regime [178][179][180][181]. It remains to be seen whether these approaches can be extended to open dissipative and decohering many-body quantum systems as well [182], analogues to the general technique reported in sec.…”

Section: Discussionmentioning

confidence: 99%

“…8. Another interesting aspect would be the investigation of tilted many-body Bose-Hubbard models including more than one energy band [180], which are naturally open systems due to decay into the continuum of free states accelerated by the tilting force [183], see also [184] in the context of continuum coupling.…”

Section: Discussionmentioning

confidence: 99%

The dissipative Bose-Hubbard model

Kordas

Witthaut

Buonsante

et al. 2015

Eur. Phys. J. Spec. Top.

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Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counterintuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.

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“…they thermalize. There has been much interest in observing and understanding the microscopic onset of thermalization and in defining the characteristic properties that qualify a system as being a bath [1][2][3][4][5][6][7][8][9][10][11][12][13]. Recently it has been demonstrated that even three degrees of freedom can serve as a bath, provided that they are chaotic, and a fourth degree of freedom can thermalize if it is coupled to this bath [2].…”

Section: Introductionmentioning

confidence: 99%

Threshold coupling strength for equilibration between small systems

Bürkle

Anglin

2019

Phys. Rev. A

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In this paper we study the thermal equilibration of small bipartite Bose-Hubbard systems, both quantum mechanically and in mean-field approximation. In particular we consider small systems composed of a single-mode "thermometer" coupled to a three-mode "bath", with no additional environment acting on the four-mode system, and test the hypothesis that the thermometer will thermalize if and only if the bath is chaotic. We find that chaos in the bath alone is neither necessary nor sufficient for equilibration in these isolated four-mode systems. The two subsystems can thermalize if the combined system is chaotic even when neither subsystem is chaotic in isolation, and under full quantum dynamics there is a minimum coupling strength between the thermometer and the bath below which the system does not thermalize even if the bath itself is chaotic. We show that the quantum coupling threshold scales like 1/N (where N is the total particle number), so that the classical results are obtained in the limit N → ∞.

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Quantum diffusion and thermalization at resonant tunneling

Cited by 19 publications

References 42 publications

Spectral analysis of two-dimensional Bose-Hubbard models

Spectral analysis of two-dimensional Bose-Hubbard models

The dissipative Bose-Hubbard model

Threshold coupling strength for equilibration between small systems

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