Chaos due to symmetry-breaking in deformed Poisson ensemble

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.

Automated summary

The competition between the strength and correlation of coupling terms in a Hamiltonian leads to phenomenological models that exhibit spectral properties between those of integrable and chaotic ensembles. Understanding the evolution of off-diagonal terms in a Hamiltonian as the symmetries of an integrable system are broken is important. We introduce a deformed Poisson ensemble that maps the coupling terms to the underlying symmetries of the Hamiltonian, and predict a chaotic limit using the maximum entropy principle, which is verified numerically.