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Abstract

Understanding the entanglement of radiation in QFT has been a long standing
challenge in high energy physics, with implications ranging from black hole
thermodynamics to quantum information. Progress has been traditionally limited
to consideration of either universal quantities fixed by symmetries, or global
properties of the asymptotic states. Here we demonstrate how the free fermion
in $1+1$-dimensions allows to go beyond by revealing the details of the density
matrix of the radiation produced by a moving mirror, that in general breaks all
conformal symmetries. We achieve this by using the resolvent method rather than
standard CFT techniques, and derive closed expressions for the R\'enyi
entropies, modular Hamiltonian and flow of the radiation. We determine the
conditions under which mirrors generate unitary transformations, leading to
Page curves resembling those expected from black hole evaporation. These
results also yield the R\'enyi entropies on AdS$_2$ with reflecting asymptotic
boundary conditions, which have applications to recent discussions of Hawking
radiation. The results are ready to be used for a variety of applications in
the field.