Interpolating between the Bose-Einstein and the Fermi-Dirac distributions in odd dimensions

TL;DR

This paper investigates how a uniformly accelerated detector in flat spacetime responds to scalar fields in various dimensions, revealing a transition between Bose-Einstein and Fermi-Dirac distributions depending on the spacetime dimension and coupling strengths.

Contribution

It demonstrates the interpolation between Bose-Einstein and Fermi-Dirac distributions in odd dimensions by adjusting coupling strengths, highlighting the thermal nature of the detector response.

Findings

Detector response is Bose-Einstein in even dimensions.

Both Bose-Einstein and Fermi-Dirac factors appear in odd dimensions.

Adjusting coupling strengths interpolates between distributions.

Abstract

We consider the response of a uniformly accelerated monopole detector that is coupled to a superposition of an odd and an even power of a quantized, massless scalar field in flat spacetime in arbitrary dimensions. We show that, when the field is assumed to be in the Minkowski vacuum, the response of the detector is characterized by a Bose-Einstein factor in even spacetime dimensions, whereas a Bose-Einstein as well as a Fermi-Dirac factor appear in the detector response when the dimension of spacetime is odd. Moreover, we find that, it is possible to interpolate between the Bose-Einstein and the Fermi-Dirac distributions in odd spacetime dimensions by suitably adjusting the relative strengths of the detector's coupling to the odd and the even powers of the scalar field. We point out that the response of the detector is always thermal and we, finally, close by stressing the apparent nature of the appearance of the Fermi-Dirac factor in the detector response.