Analytic model of thermalization: Quantum emulation of classical cellular automata

TL;DR

This paper presents a quantum emulation method for classical cellular automata, demonstrating thermalization in a solvable quantum many-body system and challenging existing thermalization theories.

Contribution

It introduces a new quantum emulation approach for classical cellular automata and provides explicit solutions to analyze thermalization mechanisms.

Findings

The quantum system thermalizes despite all eigenstates being solvable.

Eigenstate thermalization hypothesis does not explain thermalization here.

Large effective dimension scenario also fails to account for thermalization.

Abstract

We introduce a novel method of quantum emulation of a classical reversible cellular automaton. By applying this method to a chaotic cellular automaton, the obtained quantum many-body system thermalizes while all the energy eigenstates and eigenvalues are solvable. These explicit solutions allow us to verify the validity of some scenarios of thermalization to this system. We find that two leading scenarios, the eigenstate thermalization hypothesis scenario and the large effective dimension scenario, do not explain thermalization in this model.