Uniformly Accelerated Mirrors. Part 1: Mean Fluxes

TL;DR

This paper introduces an alternative model for analyzing the scattering of a massless field by a uniformly accelerated mirror, resolving divergences in flux and Bogoliubov coefficients by using an action-based approach with switching functions.

Contribution

It presents a new regularization method for the Davies-Fulling model, enabling analytical expressions for scattering amplitudes and fluxes, and links these to accelerated detector transition amplitudes.

Findings

Regularized scattering amplitudes are well-defined as distributions.

Switching functions allow control over transient behaviors.

The model unifies physics of accelerated mirrors and detectors.

Abstract

The Davies-Fulling model describes the scattering of a massless field by a moving mirror in 1+1 dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blue shift effects associated with the horizons. On one hand, the Bogoliubov coefficients are ill-defined and the total energy emitted diverges. On the other hand, the instantaneous mean flux vanishes. To obtained well-defined expressions we introduce an alternative model based on an action principle. The usefulness of this model is to allow to switch on and off the interaction at asymptotically large times. By an appropriate choice of the switching function, we obtain analytical expressions for the scattering amplitudes and the fluxes emitted by the mirror. When the coupling is constant, we recover the vanishing flux. However it is now followed by transients which inevitably become singular when the switching off is performed at late time. Our analysis reveals that the scattering amplitudes (and the Bogoliubov coefficients) should be seen as distributions and not as mere functions. Moreover, our regularized amplitudes can be put in a one to one correspondence with the transition amplitudes of an accelerated detector, thereby unifying the physics of uniformly accelerated systems. In a forthcoming article, we shall use our scattering amplitudes to analyze the quantum correlations amongst emitted particles which are also ill-defined in the Davies-Fulling model in the presence of horizons.