Dynamical Casimir Effect and the Black Body Spectrum

TL;DR

This paper investigates particle creation by a moving mirror in 2D spacetime, revealing that semitransparent mirrors produce fermionic statistics in black body radiation, contrasting with the bosonic case for perfect reflectors.

Contribution

It provides an exact calculation showing that semitransparent mirrors induce Fermi-Dirac statistics in black body radiation, challenging previous assumptions of purely bosonic emission.

Findings

Perfect mirrors emit Bose-Einstein distributed particles.

Semitransparent mirrors emit Fermi-Dirac distributed particles.

The statistics depend on the mirror's reflectivity parameter lpha.

Abstract

Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a specified trajectory, and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [$r(w)=-i\alpha/(\w+i\alpha)$ and $s(w)=\w/(\w+i\alpha)$, with $\alpha\geq 0$], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when $\alpha$ is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with previous results in the literature. However, when $\alpha$ is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. Possible consequences of this result are envisaged.