Statistics of phase space localization measures and quantum chaos in the kicked top model
arXiv:2303.05216 · doi:10.1103/PhysRevE.107.054213
Abstract
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.
arXiv comment13 pages, 8 figures
References in corpus (85)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Random Matrix Theories in Quantum Physics: Common Concepts
- Anderson Transitions
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Local conservation laws and the structure of the many-body localized states
- Eigenstate Thermalization Hypothesis
- Long-time behavior of periodically driven isolated interacting lattice systems
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Alternatives to Eigenstate Thermalization
- Ergodic dynamics and thermalization in an isolated quantum system
- Semiclassical Foundation of Universality in Quantum Chaos
- Solution of a minimal model for many-body quantum chaos
- Finite-size scaling of eigenstate thermalization
- Quantum Many-Body Scars: A Quasiparticle Perspective
- Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Entanglement as a signature of quantum chaos
- Many-body quantum chaos: Analytic connection to random matrix theory
- Spectral statistics and many-body quantum chaos with conserved charge
- Krylov complexity from integrability to chaos
- Fidelity Decay as an Efficient Indicator of Quantum Chaos
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Misleading signatures of quantum chaos
- Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
- Many-Body Chaos in the Sachdev-Ye-Kitaev Model
- Black holes, complexity and quantum chaos
- Spectral form factors and late time quantum chaos
- Bridging entanglement dynamics and chaos in semiclassical systems
- Extended nonergodic states in disordered many-body quantum systems
- Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
- Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
- Gauging classical and quantum integrability through out-of-time ordered correlators
- Joint probability densities of level spacing ratios in random matrices
- Probing symmetries of quantum many-body systems through gap ratio statistics
- Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
- Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
- Chaos and ergodicity across the energy spectrum of interacting bosons
- Multifractality meets entanglement: relation for non-ergodic extended states
- Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
- Ubiquitous quantum scarring does not prevent ergodicity
- Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
- Quantum chaos and entanglement in ergodic and non-ergodic systems
- Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
- On the structure of typical states of a disordered Richardson model and many-body localization
- Statistical properties of eigenstate amplitudes in complex quantum systems
- Localization in Fock space: A finite size scaling hypothesis for many particle excitation statistics
- Diagnosing quantum chaos in many-body systems using entanglement as a resource
- Transition from Quantum Chaos to Localization in Spin Chains
- Quantum coherence as a signature of chaos
- Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
- Delocalization and quantum chaos in atom-field systems
- Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
- Dynamical localization in chaotic systems: spectral statistics and localization measure in the kicked rotator as a paradigm for time-dependent and time-independent systems
- Quantum localization of chaotic eigenstates and the level spacing distribution
- Interacting bosons in a triple well: Preface of many-body quantum chaos
- Regular and Irregular States in Generic Systems
- Exploring phase space localization of chaotic eigenstates via parametric variation
- Chaos and quantum scars in a coupled top model
- Signatures of Chaos in Non-integrable Models of Quantum Field Theory
- Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard
- Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
- Nonlinear dynamics and quantum chaos of a family of kicked -spin models
- Effects of stickiness in the classical and quantum ergodic lemon billiard
- Multifractality in quasienergy space of coherent states as a signature of quantum chaos
- Theoretical estimates for the largest Lyapunov exponent of many-particle systems
- Quantum localization measures in phase space
- Multipartite-Entanglement Dynamics in Regular-to-Ergodic Transition: a Quantum-Fisher-Information approach
- Long-range level correlations in quantum systems with finite Hilbert space dimension
- Signatures of quantum chaos in low-energy mixtures of few fermions
- Probing the edge between integrability and quantum chaos in interacting few-atom systems
- Phenomenology of quantum eigenstates in mixed-type systems: lemon billiards with complex phase space structure
- Spectral form factor in the double-scaled SYK model
- The level repulsion exponent of localized chaotic eigenstates as a function of the classical transport time scales in the stadium billiard
- The distribution of localization measures of chaotic eigenstates in the stadium billiard
- Identification of quantum scars via phase-space localization measures
- Eigenstate thermalization scaling in approaching the classical limit
- Classical and quantum mixed-type lemon billiards without stickiness
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- Statistical and dynamical aspects of quantum chaos in a kicked Bose-Hubbard dimer
- Probing quantum chaos with the entropy of decoherent histories
- A Floquet analysis perspective of driven light-matter interaction models
- Correspondence principle, dissipation, and Ginibre ensemble
- Phase-space localization at the lowest Landau level
- Quantum-to-Classical Transition via Single-Shot Generalized Measurements
- Floquet thermalization by power-law induced permutation symmetry breaking
- Long-time signatures of chaos in large atom-light frequency ratios Rabi model