Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang, Qian; Robnik, Marko

doi:10.3390/e23101347

Cited by 13 publications

(3 citation statements)

References 139 publications

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“…The system we have focused on in this work is the kicked top model, which represents one of the prototypical models in studying quantum chaos [1] and has been realized in different experimental platforms [88][89][90]. Recently, we have studied it in the perspective of multifractal dimensions (entropies) of coherent states in the quasi-energy space [91]. These entropies describe the localization of the coherent states in the eigenbasis of the Floquet operator.…”

Section: Kicked Top Modelmentioning

confidence: 99%

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: Kicked Top Modelmentioning

confidence: 99%

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

Wang¹,

Robnik²

2023

Preprint

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“…The GOE eigenstates are fully delocalized random vectors with real components consisting of independent Gaussian random numbers. Hence, the deviation of the eigenvector structure from Gaussian behavior is an alternative benchmark to certify quantum chaos [ 42 , 86 , 87 , 88 , 89 ].…”

Section: Structure Of Eigenstatesmentioning

confidence: 99%

Quantum Chaos in the Extended Dicke Model

Wang

2022

Entropy

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We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom–atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.

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“…The GOE eigenstates are fully delocalized random vectors with real components consist of independent Gaussian random numbers. Hence, the deviation of eigenvector structure from Gaussian behavior is an alternative benchmark to certify quantum chaos [42,[86][87][88][89].…”

Section: Structure Of Eigenstatesmentioning

confidence: 99%

Quantum Chaos in the Extended Dicke Model

Wang

2022

Preprint

View full text Add to dashboard Cite

We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom-atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.

show abstract

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Cited by 13 publications

References 139 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

Quantum Chaos in the Extended Dicke Model

Quantum Chaos in the Extended Dicke Model

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