Chaos in the three-site Bose-Hubbard model -- classical vs quantum

Nakerst, Goran; Haque, Masudul

doi:10.48550/arxiv.2203.09953

Cited by 2 publications

(2 citation statements)

References 83 publications

(108 reference statements)

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“…The components of a GOE eigenstate,

, are random numbers that are uniformly distributed on a unit sphere with dimension

. In the limit

, the dependence between components vanishes, and the distribution of components can be well described by a Gaussian distribution with zero mean and variance

[ 77 , 90 , 91 , 92 ],

In the chaotic systems, it has been known that the coefficients of the mid-spectrum eigenstates are distributed as a near-Gaussian distribution [ 77 , 78 , 93 , 94 , 95 ], while the coefficients’ distribution for the eigenstates of nonchaotic systems and the edge eigenstates of chaotic systems is significantly different from Gaussian distribution [ 95 , 96 , 97 ]. As increasing

leads to the onset of chaos in the model; one would expect that the distribution of mid-spectrum eigenstates coefficients should be turned from non-Gaussian into near-Gaussian.…”

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.

show abstract

“…The components of a GOE eigenstate,

, are random numbers that are uniformly distributed on a unit sphere with dimension

. In the limit

, the dependence between components vanishes, and the distribution of components can be well described by a Gaussian distribution with zero mean and variance

[ 77 , 90 , 91 , 92 ],

leads to the onset of chaos in the model; one would expect that the distribution of mid-spectrum eigenstates coefficients should be turned from non-Gaussian into near-Gaussian.…”

Section: Structure Of Eigenstatesmentioning

confidence: 99%

Quantum Chaos in the Extended Dicke Model

Wang

2022

Entropy

View full text Add to dashboard Cite

show abstract

“…The components of a GOE eigenstate, {c ν }, are random numbers that are uniformly distributed on a unit sphere with dimension D − 1. In the limit D ≫ 1, the dependence between components vanishes and the distribution of components can be well described by a Gaussian distribution with zero mean and variance 1/D [77,[90][91][92],…”

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

Chaos in the three-site Bose-Hubbard model -- classical vs quantum

Cited by 2 publications

References 83 publications

Quantum Chaos in the Extended Dicke Model

Quantum Chaos in the Extended Dicke Model

Quantum Chaos in the Extended Dicke Model

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