Solvable models of many-body chaos from dual-Koopman circuits

TL;DR

This paper introduces classical dual-Koopman circuits as counterparts to quantum dual-unitary circuits, demonstrating their chaotic behavior and mixing properties through analytical examples like coupled standard maps and cat-map lattices.

Contribution

It defines dual-canonical transformations and dual-Koopman operators, establishing a classical framework for many-body chaos analogous to quantum models, with explicit examples and properties.

Findings

Correlations vanish outside the light cone and decay rates are governed by a simple map.

Coupled standard maps are shown to be mixing in the thermodynamic limit.

A cat-map lattice can be a Bernoulli system, indicating maximal chaos.

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 define their classical counterparts as dual-canonical transformations and associated dual-Koopman operators. Like their quantum counterparts, 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.