Interacting bosons in a triple well: Preface of many-body quantum chaos

W., Karin Wittmann; Castro, Erick; Foerster, Angela; Santos, Lea F.

doi:10.1103/physreve.105.034204

Cited by 22 publications

(12 citation statements)

References 106 publications

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“…Unveiling how the statistics of the localization measures of eigenstates is affected by underlying chaos would help us get deep understanding on the signatures of quantum chaos and opens up a new way to distinguish between regular and chaotic dynamics in quantum systems. An interesting extension of this work is to explore how our results change in the many body quantum chaotic systems, such as the coupled top model [18], Dicke model [84][85][86], and Bose-Hubbard model [21,22,132]. Another open question that deserves examination is to study the correlation between the phase space localization measures and the entanglement entropy in quantum chaotic systems.…”

Section: Discussionmentioning

confidence: 95%

Statistics of phase space localization measures and quantum chaos in the kicked top model

Wang¹,

Robnik²

2023

Preprint

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Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi functions), we explore the characterizations of quantum chaos using the statistics of the localization measures. We consider the paradigmatic kicked top model, which shows a transition to chaos with increasing the kicking strength. We demonstrate that the distributions of the localization measures exhibit a drastic change as the system undergoes the crossover from integrability to chaos. We also show how to identify the signatures of quantum chaos from the central moments of the distributions of localization measures. Moreover, we find that the localization measures in the fully chaotic regime apparently exhibit universally the beta distribution, in agreement with previous studies in the billiard systems and the Dicke model. Our results contribute to a further understanding of quantum chaos and shed light on the usefulness of the statistics of phase space localization measures in diagnosing the presence of quantum chaos, as well as the localization properties of eigenstates in quantum chaotic systems.

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Section: Discussionmentioning

confidence: 95%

Statistics of phase space localization measures and quantum chaos in the kicked top model

Wang¹,

Robnik²

2023

Preprint

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“…According to the central limit theorem, a large sum of independent random numbers follows a Gaussian distribution, so in the region where the eigenstates are chaotic, the distribution of O k,k should be Gaussian. This has been confirmed for different chaotic systems with many-degrees of freedom [15,86,87], but not in chaotic systems with one [88] or few particles [89], few degrees of freedom [90] or in many-body systems when Ô is not few-body [91].…”

Section: Thermalization In the Dicke Modelmentioning

confidence: 96%

Chaos and Thermalization in the Spin-Boson Dicke Model

Villaseñor¹,

Pilatowsky-Cameo²,

Bastarrachea-Magnani³

et al. 2022

Preprint

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We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.

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“…In fact, the dimer is integrable since there are two conserved quantities, the Hamiltonian itself and the total number of bosons, which answers why the dimer BHM can be exactly solved by using the simple Bethe ansatzes [23,24]. However, the addition of a further site to the dimer yielding either a linear chain with open boundary condition or a ring with periodic boundary condition makes the resulting inhomogenous trimer non-integrable due to a lack of sufficient conserved quantities [27,28], which in general leads to a chaotic spectrum [18,29,30] due to the occurrence of level-repulsion and the appearance of states not obtainable from a semiclassical method, such as the Einstein-Brillouin-Keller method [27]. Similarly, the superfluid-stability and chaoticity of the trimer BHM in a rotating frame…”

Section: Introductionmentioning

confidence: 99%

An exact solution of the homogenous trimer Bose-Hubbard model

Pan¹,

Li²,

Wu³

et al. 2023

J. Stat. Mech.

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It is shown that the homogenous three-site (trimer) Bose–Hubbard model with a periodic boundary condition can be solved exactly by using an extended Bethe ansatz based on the solution of the dimer model and the site-permutation symmetry. A solution of the model within the S 3 symmetric or non-symmetric subspace is presented. Coupled differential equations of a series of extended Heine–Stieltjes polynomials, the zeros of which are related to the solution of the model, are derived. Numerical examples of the solution of the model with N ⩽ 4 bosons, including the related Heine–Stieltjes polynomials and the Van Vleck polynomials, are presented, which serve to validate the procedure and illustrate the completeness of the solutions they render.

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Interacting bosons in a triple well: Preface of many-body quantum chaos

Cited by 22 publications

References 106 publications

Statistics of phase space localization measures and quantum chaos in the kicked top model

Statistics of phase space localization measures and quantum chaos in the kicked top model

Chaos and Thermalization in the Spin-Boson Dicke Model

An exact solution of the homogenous trimer Bose-Hubbard model

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