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 those Poisson (integrable) Wigner-Dyson (chaotic) ensembles. It is important to understand how the off-diagonal evolve as one or more symmetries an integrable system are explicitly broken. We introduce deformed ensemble demonstrate exact mapping underlying Hamiltonian. From maximum entropy principle we predict chaotic limit which numerically verified from survival probability calculations.