Uncertainty principle in a cavity at finite temperature

TL;DR

This paper investigates how the uncertainty principle behaves for a quantum system in a heated cavity, revealing oscillatory behavior of the momentum-position product that differs from free space dynamics.

Contribution

It introduces a dressed state approach to analyze the uncertainty principle at finite temperature within a cavity, highlighting oscillatory behavior and finite minima/maxima over time.

Findings

Oscillatory behavior of the uncertainty product in a small heated cavity.

Periodic finite minima and maxima of the uncertainty product.

Contrast with free space where the product approaches a constant asymptotically.

Abstract

We employ a dressed state approach to perform a study on the behavior of the uncertainty principle for a system in a heated cavity. We find, in a small cavity for a given temperature, an oscillatory behavior of the momentum--coordinate product, $(\Delta\,p)\,(\Delta\,q)$, which attains periodically finite absolute minimum (maximum) values, no matter large is the elapsed time. This behavior is in a sharp contrast with what happens in free space, in which case, the product $(\Delta\,p)\,(\Delta\,q)$ tends asymptotically, for each temperature, to a constant value, independent of time.