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

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.

46 pages, 21 figures, long appendix includes the perturbation theory calculation details

References in corpus (6)

• Typicality for Generalized Microcanonical Ensembles
• Decoherence in adiabatic quantum computation
• Thermal equilibration between two quantum systems
• Dynamics of thermalisation in small Hubbard-model systems
• Quantum Decoherence Scaling with Bath Size: Importance of Dynamics, Connectivity, and Randomness
• How ubiquitous are dragon segments in quantum transmission?

Cited by in corpus (6)

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• Initial-state-dependent thermalization in open qubits
• Finite thermal reservoirs and the canonical distribution
• Optimized Sampling of Mixed-State Observables