Solvable Models of Many-Body Chaos from Dual-Koopman Circuits.

Abstract

Dual-unitary circuits are being vigorously studied as models of many-body quantum chaos that can be solved exactly for correlation functions and time evolution of states. Here we study their classical counterparts defining dual-canonical transformations and associated dual-Koopman operators. Classical many-body systems constructed from these have the property, like their quantum counterparts, that the correlations vanish everywhere except on the light cone, on which they decay with rates governed by a simple contractive map. Providing a large class of such dual-canonical transformations, we study in detail the example of a coupled standard map and show analytically that arbitrarily away from the integrable case, in the thermodynamic limit the system is mixing. We also define "perfect" Koopman operators that lead to the correlation vanishing everywhere including on the light cone and provide an example of a cat-map lattice which would qualify to be a Bernoulli system at the apex of the ergodic hierarchy.