Vacuum fluctuations of a scalar field near a reflecting boundary and their effects on the motion of a test particle

TL;DR

This paper investigates how quantum vacuum fluctuations of a scalar field near a reflecting boundary influence a test particle's motion, highlighting the effects of switching functions and boundary conditions on quantum dispersions and energy changes.

Contribution

It introduces a detailed analysis of vacuum fluctuation effects on particle motion near a boundary, emphasizing the role of switching functions in regularizing divergences and understanding energy modifications.

Findings

Dispersions occur only with a boundary present.

Smooth switching functions regularize divergences.

Transition speed affects particle energy changes.

Abstract

The contribution from quantum vacuum fluctuations of a real massless scalar field to the motion of a test particle that interacts with the field in the presence of a perfectly reflecting flat boundary is here investigated. There is no quantum induced dispersions on the motion of the particle when it is alone in the empty space. However, when a reflecting wall is introduced, dispersions occur with magnitude dependent on how fast the system evolves between the two scenarios. A possible way of implementing this process would be by means of an idealized sudden switching, for which the transition occurs instantaneously. Although the sudden process is a simple and mathematically convenient idealization it brings some divergences to the results, particularly at a time corresponding to a round trip of a light signal between the particle and the wall. It is shown that the use of smooth switching functions, besides regularizing such divergences, enables us to better understand the behavior of the quantum dispersions induced on the motion of the particle. Furthermore, the action of modifying the vacuum state of the system leads to a change in the particle energy that depends on how fast the transition between these states is implemented. Possible implications of these results to the similar case of an electric charge near a perfectly conducting wall are discussed.