Quantum localization measures in phase space

Villaseñor, David; Pilatowsky-Cameo, Saúl; Bastarrachea-Magnani, Miguel A.; Lerma-Hernández, Sergio; Hirsch, Jorge G.

doi:10.1103/physreve.103.052214

Cited by 19 publications

(12 citation statements)

References 80 publications

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“…( 1) and α 0 is the Rényi index. It has been shown that the exponential of S α acts as an useful indicator of the degree of localization of the system in phase space, from which the Rényi volume of order α term has been coined [86]. In our work, we can see that S α tends to W as α → 1, while M 2 = exp(−S 2 ).…”

Section: Husimi Functionsupporting

confidence: 49%

Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Wang

Pérez‐Bernal

2021

Phys. Rev. E

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Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.

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Section: Husimi Functionsupporting

confidence: 49%

Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Wang

Pérez‐Bernal

2021

Phys. Rev. E

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“…Substituting the sums ∞ i=1 φ i |ρ|φ i α in Eq. ( 7) by these averages, we obtain the Rényi occupations of order α ≥ 0 [77],…”

Section: Rényi Occupationsmentioning

confidence: 99%

“…If one wishes to investigate maximally delocalized states in these systems, one must define a finite region as a reference volume. There are multiple ways to select this bounded region, and each choice produces a different localization measure [77,79]. A natural volume of reference is obtained by measuring the degree of localization of a quantum state over the classical phase-space energy shell, as proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Identification of quantum scars via phase-space localization measures

Santos

Pilatowsky-Cameo

̃nor

et al. 2022

Quantum

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There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the α-moments of the Husimi function and is known as the Rényi occupation of order α. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spin-boson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with α>1 are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments (α>1) of the Husimi function, we are able to identify qualitatively and quantitatively the unstable periodic orbits that scar some of the eigenstates of the model.

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“…Since a generic system usually has a structured phase space with coexistence of regular and chaotic regions rather than a featureless fully developed chaotic region, it is highly desirable to investigate such quantities that enable us to analyze the local chaotic behaviors of a quantum system. With the help of coherent states (or localized wave packets), the local chaotic behaviors of quantum systems have been extensively explored in a variety of works [42][43][44][45][46][47][48][49]. Here, by considering the kicked top model, we are interested in how to reveal the phase space structures and the degree of chaos by means of multifractality of coherent states.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Robnik

2021

Entropy

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

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Quantum localization measures in phase space

Cited by 19 publications

References 80 publications

Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Identification of quantum scars via phase-space localization measures

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

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