Time Dependent Quantum Thermodynamics of a Coupled Quantum Oscillator System in a Small Thermal Environment

TL;DR

This study simulates a small quantum system of coupled oscillators interacting with a designed environment, demonstrating thermalization, entropy increase, and the relationship between quantum coherence and temperature.

Contribution

It introduces a model of a quantum oscillator system with a tailored environment, showing how entanglement leads to thermalization and the loss of quantum coherence.

Findings

System reaches a Boltzmann distribution with effective temperatures close to the designed temperature.

All initial states equilibrate at similar rates, losing memory of initial conditions.

Quantum coherence is eliminated only at maximal entropy, corresponding to infinite temperature.

Abstract

Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is argued, contrary to common understanding, that quantum interference and coherence are eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.