Quantum relaxation in a system of harmonic oscillators with time-dependent coupling

TL;DR

This paper investigates how nonequilibrium quantum states in a system of time-dependent coupled harmonic oscillators tend to relax to equilibrium, analyzing the influence of various parameters through numerical simulations within the de Broglie-Bohm framework.

Contribution

It provides a detailed numerical analysis of quantum relaxation in coupled harmonic oscillators with time-dependent interactions, highlighting parameter effects on relaxation times.

Findings

Relaxation generally occurs but can be slowed by certain parameters.

Stronger coupling tends to delay relaxation.

Implications for detecting relic nonequilibrium systems are discussed.

Abstract

In the context of the de Broglie-Bohm pilot wave theory, numerical simulations for simple systems have shown that states that are initially out of quantum equilibrium - thus violating the Born rule - usually relax over time to the expected $|\psi|^2$ distribution on a coarse-grained level. We analyze the relaxation of nonequilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators in which the coupling depends explicitly on time through numerical simulations, focusing in the influence of different parameters such as the number of modes, the coarse-graining length and the coupling constant. We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters, particularly to the one related to the strength of the interaction. Possible implications on the detection of relic nonequilibrium systems are discussed.