Excitation of an Atom by a Uniformly Accelerated Mirror through Virtual Transitions.

We find that uniformly accelerated motion of a mirror yields excitation of a static two-level atom with simultaneous emission of a real photon. This occurs because of virtual transitions with probability governed by the Planck factor involving the photon frequency ν and the Unruh temperature. The result is different from the Unruh radiation of an accelerated atom, which is governed by the frequency of the atom, ω, rather than frequency of the emitted photon. We also find that the excitation probability oscillates as a function of the atomic position because of interference between contributions from the waves incident on and reflected from the mirror.

Quantum optics approach to radiation from atoms falling into a black hole.

We show that atoms falling into a black hole (BH) emit acceleration radiation which, under appropriate initial conditions, looks to a distant observer much like (but is different from) Hawking BH radiation. In particular, we find the entropy of the acceleration radiation via a simple laser-like analysis. We call this entropy horizon brightened acceleration radiation (HBAR) entropy to distinguish it from the BH entropy of Bekenstein and Hawking. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity.

Neumann nodal domains.

As an alternative to nodal domains in the usual sense, we propose a partition of the domain of a real-valued eigenfunction in R2 by trajectories of the gradient, linking saddle points to extrema. Its most elementary properties are listed and exemplified. The main point is that the problem of avoided crossings is largely eliminated.