Radiation from a receding mirror: Unruh-DeWitt detector distinguishes a Dirac fermion from a scalar boson

TL;DR

This paper demonstrates that an Unruh-DeWitt detector can distinguish between fermionic and bosonic radiation from a receding mirror, revealing Fermi-Dirac statistics through its transition rate, unlike stress-energy tensor measurements.

Contribution

It shows that a detector coupled to the scalar density of a spinor field can identify fermionic radiation, providing a new method to differentiate fermions from bosons in black hole analog models.

Findings

Detector transition rate proportional to fermionic free energy density.

Stress-energy tensor cannot distinguish fermions from bosons.

Unruh-DeWitt detector reveals Fermi-Dirac statistics in radiation.

Abstract

It is well known that a receding mirror in Minkowski spacetime can model the formation of a black hole, producing Hawking-like radiation at late times. We ask what an observer would need to do to discern whether the radiation is fermionic or bosonic. Specialising to massless fields in 1+1 dimensions, we find that an Unruh-DeWitt detector accomplishes this: the late time transition rate of a detector coupled linearly to the scalar density of a spinor field is proportional to the Helmholtz free energy density of a fermionic thermal bath, hence showing a clear sign of Fermi-Dirac statistics, with no counterpart in the response of a detector coupled linearly to a scalar field or its derivative. By contrast, an observer examining just the stress-energy tensor sees no difference between a fermion and a boson, neither at late times nor early.