Rapid spatial equilibration of a particle in a box

TL;DR

This paper demonstrates that a quantum particle in a one-dimensional box rapidly reaches equilibrium with respect to coarse-grained position measurements, with the process occurring in a time comparable to the wave packet reaching the box edges.

Contribution

It provides a detailed analysis showing rapid equilibration in a quantum particle in a box, highlighting insensitivity to measurement details and initial conditions.

Findings

Equilibration occurs quickly, within the time for the wave packet to reach the box edges.

Equilibration behavior is insensitive to measurement specifics.

The process is demonstrated for a quantum particle in a one-dimensional box.

Abstract

We study the equilibration behaviour of a quantum particle in a one-dimensional box, with respect to a coarse grained position measurement (whether it lies in a certain spatial window or not). We show that equilibration in this context indeed takes place and does so very rapidly, in a time comparable to the time for the initial wave packet to reach the edges of the box. We also show that, for this situation, the equilibration behaviour is relatively insensitive to the precise choice of position measurements or initial condition.