Quantum thermalization and equilibrium state with multiple temperatures

TL;DR

This paper explores how isolated quantum systems can reach thermal equilibrium with subsystems described by Gibbs distributions, and predicts the emergence of multiple temperatures in superposition states, with potential experimental verification.

Contribution

It introduces a theoretical framework predicting multiple-temperature equilibrium states in quantum superpositions, expanding understanding of quantum thermalization.

Findings

Subsystems follow Gibbs distribution at equilibrium

Superposition states can exhibit multiple temperatures

Experimental schemes for verification are proposed

Abstract

A large class of isolated quantum system in a pure state can equilibrate and serve as a heat bath. We show that once the equilibrium is reached, any of its subsystems that is much smaller than the isolated system is thermalized such that the subsystem is governed by the Gibbs distribution. Within this theoretical framework, the celebrated superposition principle of quantum mechanics leads to a prediction of a thermalized subsystem with multiple temperatures when the isolated system is in a superposition state of energy eigenstates of multiple distinct energy scales. This multiple-temperature state is at equilibrium, completely different from a non-equilibrium state that has multiple temperatures at different parts. Feasible experimental schemes to verify this prediction are discussed.