Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system

Lerma-Hernández, Sergio; Villaseñor, David; Bastarrachea-Magnani, Miguel A.; Torres-Herrera, E. J.; Santos, Lea F.; Hirsch, Jorge G.

doi:10.1103/physreve.100.012218

Cited by 52 publications

(55 citation statements)

References 88 publications

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“…in the form of what is known as the correlation hole [2,29,43,51,67,69,71,73,86,95,[104][105][106]111], recently referred to also as the "ramp" [27]. The correlation hole corresponds to a dip below S ∞ = n |C n | 4 , which is the infinite-time average (saturation value) of S P (t) .…”

Section: Survival Probabilitymentioning

confidence: 99%

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Probing the edge between integrability and quantum chaos in interacting few-atom systems

Fogarty

García-March

Santos

et al. 2021

Quantum

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Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

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Section: Survival Probabilitymentioning

confidence: 99%

“…In [67,95,106] a general analytic solution was derived for the survival probability for chaotic systems. For the square distribution used here, this solution is given by Here, η is the number of energy eigenvectors in the energy window ∆E.…”

Section: Survival Probabilitymentioning

confidence: 99%

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Fogarty

García-March

Santos

et al. 2021

Quantum

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“…The initial decay of the survival probability is determined by the shape and bounds of the energy distribution of the initial state [88][89][90][91]. The presence of correlated eigenvalues gets explicitly manifested later, when the dynamics resolve the discreteness of the spectrum and the mean survival probability develops a dip below its saturation point, known as correlation hole [37,[57][58][59][60][61][62][63][64][65][66][67][68][69][70], which appears also for experimental local observables [67,68]. The use of the correlation hole as an alternative to detect level repulsion was first proposed for molecules with poor line resolution [57].…”

Section: Correlation Holementioning

confidence: 99%

“…However, eigenvalues, eigenstates, and matrix elements of observables are not easily accessible to experiments that focus on time evolutions, such as those with cold atoms and ion traps. Therefore, we promote the use of the correlation hole [37,[57][58][59][60][61][62][63][64][65][66][67][68][69][70], which is a dynamical tool to capture level repulsion and spectrum rigidity. This chaos indicator does not require unfolding the spectrum or separating it by symmetries [70].…”

Section: Introductionmentioning

confidence: 99%

Speck of chaos

Santos

Pérez‐Bernal

Torres-Herrera

2020

Phys. Rev. Research

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It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional X X Z model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

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“…Its initial decay cannot distinguish systems with or without level-repulsion, a claim that has been made in the past in the context of many-body quantum systems [22][23][24]. Manifestations of the correlations between the eigenvalues emerge only at long times, in the form of the correlation hole [25][26][27][28][29][30][31][32][33][34]. The hole is not necessarily a signature of quantum chaos.…”

Section: Introductionmentioning

confidence: 99%

Level repulsion and dynamics in the finite one-dimensional Anderson model

2019

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This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal onsite disorder strength W . But this is not the case when the model is finite and the localization length is larger than the system size L, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter ξ ∝ (W 2 L) −1 . As ξ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster that when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for W = 0, when it is in fact deeper. arXiv:1904.11989v2 [cond-mat.dis-nn]

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Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system

Cited by 52 publications

References 88 publications

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Speck of chaos

Level repulsion and dynamics in the finite one-dimensional Anderson model

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