Chaos due to symmetry-breaking in deformed Poisson ensemble

Abstract

The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner-Dyson (chaotic) ensembles. It is important to understand how the off-diagonal terms of a Hamiltonian evolve as one or more symmetries of an integrable system are explicitly broken. We introduce a deformed Poisson ensemble to demonstrate an exact mapping of the coupling terms to the underlying symmetries of a Hamiltonian. From the maximum entropy principle we predict a chaotic limit which is numerically verified from the spectral properties and the survival probability calculations.

arXiv comment17 pages, 5 figures

References in corpus (23)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Random-matrix theory of Majorana fermions and topological superconductors
• Fluctuations of the inverse participation ratio at the Anderson transition
• Emergence of quantum chaos in finite interacting Fermi systems
• A random matrix model with localization and ergodic transitions
• Thouless and relaxation time scales in many-body quantum systems
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Critical quantum chaos and the one dimensional Harper model
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Spectral Statistics in the Quantized Cardioid Billiard
• Quantum integrability in systems with finite number of levels
• Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model
• Deformed Gaussian Orthogonal Ensemble description of Small-World networks
• Matrix Elements of Random Operators and Discrete Symmetry Breaking in Nuclei
• Spectral statistics of Toeplitz matrices
• Statistical analysis of chiral structured ensembles: role of matrix constraints
• Rotationally invariant ensembles of integrable matrices

Cited by in corpus (12)

• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Proposal for many-body quantum chaos detection
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Transport in deformed centrosymmetric networks
• Comparative Microscopic Study of Entropies and their Production
• Emergent multifractality in power-law decaying eigenstates
• Spectral form factor and energy correlations in banded random matrices
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Typical Positivity of Nonequilibrium Entropy Production for Pure States
• Identifying mobility edge from finite temperature spectral form factor