Perturbations and quantum relaxation

TL;DR

This paper explores how tiny perturbations in a quantum system, modeled by a 2D harmonic oscillator, can prevent relaxation to equilibrium over long periods, with potential implications for cosmology.

Contribution

It provides evidence that small perturbations can confine trajectories and inhibit quantum relaxation, extending understanding of quantum dynamics in expanding space models.

Findings

Trajectories remain highly confined despite perturbations.

Relaxation to quantum equilibrium is prevented over long timescales.

Implications for quantum behavior in cosmological settings.

Abstract

We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.