Quantum dissipative effects in moving imperfect mirrors: sidewise and normal motions

TL;DR

This paper investigates the quantum dissipative effects caused by the motion of imperfect mirrors, analyzing both normal and parallel motions, and demonstrates the existence of frictional forces during sliding motions.

Contribution

It extends the functional approach to the dynamical Casimir effect to include dissipative effects for moving imperfect mirrors in vacuum.

Findings

Frictional force exists during parallel sliding motion of mirrors.

Dissipative effects depend on the type of mirror motion (normal or parallel).

Nonlocal interaction models the internal degrees of freedom of mirrors.

Abstract

We extend our previous work on the functional approach to the dynamical Casimir effect, to compute dissipative effects due to the relative motion of two flat, parallel, imperfect mirrors in vacuum. The interaction between the internal degrees of freedom of the mirrors and the vacuum field is modeled with a nonlocal term in the vacuum field action. We consider two different situations: either the motion is `normal', i.e., the mirrors advance or recede changing the distance $a(t)$ between them; or it is `parallel', namely, $a$ remains constant, but there is a relative sliding motion of the mirrors' planes. For the latter, we show explicitly that there is a non-vanishing frictional force, even for a constant shifting speed.