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.

Dynamical signatures of Chaos to integrability crossover in 2×2 generalized random matrix ensembles

“…Since RPE is essentially Poisson ensemble perturbed by WDE, the perturbation strength can be considered as a fictitious time and RPE can be cast as a Brownian ensemble [27][28][29][30][31]. Again RPE can be considered as a deformed ensemble [32][33][34][35] where the symmetries present in an integrable system are broken. Apart from the obvious appeal as an interpolating random matrix ensemble, interestingly, RPE hosts three distinct phases: ergodic, non-ergodic extended phase having fractal eigenstates and a localized phase [36][37][38][39].…”