Decoherence and Thermalization of Quantum Spin Systems

TL;DR

This review explores how quantum spin systems undergo decoherence and thermalization through numerical solutions of the Schrödinger equation, revealing conditions for equilibrium states and supporting quantum mechanics as the basis of statistical mechanics.

Contribution

It demonstrates that pure quantum dynamics can lead to microcanonical and canonical distributions without time-averaging or weak coupling assumptions.

Findings

Environment drives system to fully decoherent state

Reduced density matrix approaches microcanonical or canonical ensemble

Decoherence correlates with maximum entropy states

Abstract

In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schr\"{o}dinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.