Dynamical Casimir effect and the black body spectrum

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) = −iα/(ω + iα) and s(w) = ω/(ω + iα), with α ⩾ 0], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when α 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 α 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.