Quantum Decoherence at Finite Temperatures

TL;DR

This paper investigates how quantum systems decohere and thermalize at finite temperatures, revealing that under certain symmetries, the system's behavior can be predicted without considering system-environment coupling at first order.

Contribution

It demonstrates that, due to Hamiltonian symmetries, first-order perturbation theory suffices to analyze decoherence and thermalization, enabling simplified expressions based on free energies.

Findings

Decoherence and thermalization measures can be predicted from uncoupled systems at first order.

Closed-form perturbative expressions relate these measures to free energies.

Numerical validation with quantum spins supports the theoretical results.

Abstract

We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The whole system is prepared in a canonical thermal state at a finite temperature. 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 the uncoupled system 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 $E$. Numerical results for both coupled and decoupled systems with up to 40 quantum spins validate these findings.