Effective Theoretical Approach to Back Reaction of the Dynamical Casimir Effect in 1+1 Dimensions

TL;DR

This paper develops an effective theoretical framework to analyze the dynamical Casimir effect in 1+1 dimensions, incorporating back-reaction effects via an analogy with cosmological models, and confirms the force's dependence on mirror velocity.

Contribution

It introduces a novel effective model that captures back-reaction in the dynamical Casimir effect using a scale factor analogy with cosmology, validated through explicit calculations.

Findings

The dynamical Casimir force depends on mirror velocity.

The force is always attractive and exceeds static Casimir force in the adiabatic regime.

The effective action includes quantum corrections from the conformal anomaly.

Abstract

We present an approach to studying the Casimir effects by means of the effective theory. An essential point of our approach is replacing the mirror separation into the size of space S^1 in the adiabatic approximation. It is natural to identify the size of space S^1 with the scale factor of the Robertson-Walker-type metric. This replacement simplifies the construction of a class of effective models to study the Casimir effects. To check the validity of this replacement we construct a model for a scalar field coupling to the two-dimensional gravity and calculate the Casimir effects by the effective action for the variable scale factor. Our effective action consists of the classical kinetic term of the mirror separation and the quantum correction derived by the path-integral method. The quantum correction naturally contains both the Casimir energy term and the back-reaction term of the dynamical Casimir effect, the latter of which is expressed by the conformal anomaly. The resultant effective action describes the dynamical vacuum pressure, i.e., the dynamical Casimir force. We confirm that the force depends on the relative velocity of the mirrors, and that it is always attractive and stronger than the static Casimir force within the adiabatic approximation.