Quantum localization measures in phase space
arXiv:2103.07480 · doi:10.1103/PhysRevE.103.052214
Abstract
Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this topic is far from being understood. There is no unique way to measure localization, and individual measures can reflect different aspects of the same quantum state. Here, we present a general scheme to define localization in measure spaces, which is based on what we call Rényi occupations, from which any measure of localization can be derived. We apply this scheme to the four-dimensional unbounded phase space of the interacting spin-boson Dicke model. In particular, we make a detailed comparison of two localization measures based on the Husimi function in the regime where the model is chaotic, namely one that projects the Husimi function over the finite phase space of the spin and another that uses the Husimi function defined over classical energy shells. We elucidate the origin of their differences, showing that in unbounded spaces the definition of maximal delocalization requires a bounded reference subspace, with different selections leading to contextual answers.
arXiv comment14 pages, 5 figures
References in corpus (43)
- Many body localization and thermalization in quantum statistical mechanics
- Anderson Transitions
- Many-body localization, thermalization, and entanglement
- Chaos and the Quantum Phase Transition in the Dicke Model
- Statistics of energy levels and eigenfunctions in disordered systems
- Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
- Multifractality and critical fluctuations at the Anderson transition
- Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
- Realization of the Dicke model using cavity-assisted Raman transitions
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Ultrastrong coupling phenomena beyond the Dicke model
- Accurate numerical solution to the finite-size Dicke model
- Universal geometric approach to uncertainty, entropy and information
- Critical parameters from generalised multifractal analysis at the Anderson transition
- Generalized Inverse Participation Ratio as a Possible Measure of Localization for Interacting Systems
- Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition
- Diffusion and localization in chaotic billiards
- Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
- Dicke model simulation via cavity-assisted Raman transitions
- Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
- Renyi-Wehrl entropies as measures of localization in phase space
- Equilibration and macroscopic quantum fluctuations in the Dicke model
- Classical chaos in atom-field systems
- Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
- Ubiquitous quantum scarring does not prevent ergodicity
- Quantum quench dynamics in Dicke superradiance models
- Dynamical signatures of quantum chaos and relaxation timescales in a spin-boson system
- Dynamics of the Dicke model close to the classical limit
- Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment
- Dynamical Localization of Coupled Relativistic Kicked Rotors
- Semiclassical coherent state propagator for systems with spin
- Extremal quantum states
- Delocalization and quantum chaos in atom-field systems
- Quantum localization of chaotic eigenstates and the level spacing distribution
- Many-Body Dynamical Localization in a Kicked Lieb-Liniger Gas
- Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard
- Multifractal wave functions of simple quantum maps
- Many-body dynamical localization in the kicked Bose-Hubbard chain
- Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring
- Analytical description of the survival probability of coherent states in regular regimes
- Quantum scarring in a spin-boson system: fundamental families of periodic orbits
- Multifractality of quantum wave functions in the presence of perturbations
Cited by in corpus (14)
- Quantum chaos and the complexity of spread of states
- Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
- Statistics of phase space localization measures and quantum chaos in the kicked top model
- Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions
- Multifractality in quasienergy space of coherent states as a signature of quantum chaos
- Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
- Phenomenology of quantum eigenstates in mixed-type systems: lemon billiards with complex phase space structure
- Identification of quantum scars via phase-space localization measures
- Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
- Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space
- Localization measures of parity adapted U()-spin coherent states applied to the phase space analysis of the -level Lipkin-Meshkov-Glick model
- Analysis of chaos and regularity in the open Dicke model
- Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach
- Phase transitions, symmetries, and tunneling in Kerr parametric oscillators