Quantum Decoherence and Thermalization at Finite Temperature within the Canonical Thermal State Ensemble

TL;DR

This paper investigates how quantum systems decohere and thermalize at finite temperatures within a canonical ensemble, revealing that these processes are finite and predictable even in large systems, with simplified models capturing key behaviors.

Contribution

It demonstrates that decoherence and thermalization measures can be accurately predicted using perturbation theory considering system-environment symmetries, simplifying the analysis of complex quantum systems.

Findings

Decoherence and thermalization measures remain finite at finite temperature in the thermodynamic limit.

First-order perturbation theory with respect to coupling strength suffices under common symmetries.

Numerical results support the theoretical predictions for systems with up to 40 quantum spins.

Abstract

We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The entirety $S$$+$$E$ is prepared in a canonical thermal state at a finite temperature, that is the entirety is in a steady state. Both our numerical results and theoretical predictions show that measures of the decoherence and the thermalization of $S$ are generally finite, even in the thermodynamic limit, when the entirety $S$$+$$E$ is at finite temperature. Notably, applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider $S$ uncoupled from $E$, but entangled with $E$, to predict decoherence and thermalization measures of $S$. This decoupling allows closed form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of $S$ and of $E$. Large-scale numerical results for both coupled and uncoupled entireties with up to 40 quantum spins support these findings.