Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

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

doi:10.1088/1367-2630/ab8ef8

Cited by 37 publications

(35 citation statements)

References 100 publications

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“…In these cases, the approach to the asymptotic value of S P ( t ) is much smoother and exhibits the so-called correlation hole, which corresponds to the ramp towards saturation. The correlation hole reflects the presence of correlated eigenvalues and is a quantum signature of classical chaos 57 – 59 .…”

Section: Resultsmentioning

confidence: 99%

“…The coherent states are described by four coordinates x = ( q , p ; Q , P ). To select coherent states at a given energy ϵ , we solve the second-degree equation h cl ( q , p ; Q , P ) = ϵ for q , which yields two solutions 59 . All of the initial coherent states shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…We use where ν ( E ) is the density of states, ρ ( E ) is a Gaussian profile of width j σ centered at energy j ϵ , and M ensures normalization. This way, has a defined energy center ϵ , where the Husimi projection and the localization measure are calculated 59 , 70 .…”

Section: Methodsmentioning

confidence: 99%

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Ubiquitous quantum scarring does not prevent ergodicity

et al. 2021

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In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born’s rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Ubiquitous quantum scarring does not prevent ergodicity

et al. 2021

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“…The Dicke model [30] was initially introduced to explain the phenomenon of superradiance [36,43,50,80] and has since fostered a wide variety of theoretical studies, including the behavior of out-of-time-ordered correlators [24,59,63], manifestations of quantum scarring [6,29,35,64,65], non-equilibrium dynamics [1,50,51,57,58,78], and measures of quantum localization with respect to phase space [65,79]. The model is also of great interest to experiments with trapped ions [26,71], superconducting circuits [47], and cavity assisted Raman transitions [5,82].…”

Section: Dicke Modelmentioning

confidence: 99%

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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“…As described in Ref. [36] and Appendix D, both quantities can be evaluated classically by using the classical equations through the so called Truncated Wigner Approximation (TWA).…”

Section: B Evolution Of Observables and Breaking Of The Classical-qua...mentioning

confidence: 99%

Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

Nader,

González-Rodríguez,

Lerma-Hernández

2021

Preprint

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Using the Wherl entropy, we study the delocalization in phase-space of energy eigenstates in the vicinity of avoided crossing in the Lipkin-Meshkov-Glick model. These avoided crossing, appearing at intermediate energies in a certain parameter region of the model, originate classically from pairs of trajectories lying in different phase space regions, which contrary to the low energy regime, are not connected by the discrete parity symmetry of the model. As coupling parameters are varied, a sudden increase of the Wherl entropy is observed for eigenstates close to the critical energy of the excited-state quantum phase transition (ESQPT). This allows to detect when an avoided crossing is accompanied by a superposition of the pair of classical trajectories in the Husimi functions of eigenstates. This superposition yields an enhancement of dynamical tunneling, which is observed by considering initial Bloch states that evolve partially into the partner region of the paired classical trajectories, thus breaking the quantum-classical correspondence in the evolution of observables.

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Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

Cited by 37 publications

References 100 publications

Ubiquitous quantum scarring does not prevent ergodicity

Ubiquitous quantum scarring does not prevent ergodicity

Identification of quantum scars via phase-space localization measures

Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

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