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

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.

26 pages. v3: Corrected a technical oversight in Appendix B.1 that doesn't affect the results. Published in CQG

References in corpus (6)

• How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile
• Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?
• Onset and decay of the 1+1 Hawking-Unruh effect: what the derivative-coupling detector saw
• Black Hole Evaporation in an Expanding Universe
• Unruh-DeWitt detector's response to fermions in flat spacetimes
• Eternal and Evanescent Black Holes: It's All Done With Mirrors

Cited by in corpus (3)

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• The cost of building a wall for a fermion