Scattering approach to the dynamical Casimir effect

We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries and dispersive objects in relative motion. A general (trace) formula is derived for the radiation from accelerating boundaries. Applications are provided for objects with different shapes in various dimensions, and undergoing rotational or linear motion. Within this framework, photon generation is discussed in the context of a modulated optical mirror. For dispersive objects, we find general results solely in terms of the scattering matrix. Specifically, we discuss the vacuum friction on a rotating object, and the friction on an atom moving parallel to a surface.

Figure 1

A segment in a waveguide. The arrows indicate the direction along which the segment oscillates. Below a certain frequency, ${\omega }_{\min }=2{\omega }_0$, the motion is frictionless.

Figure 2

An (asymmetrical) spinning object. The object slows down as it emits “photons.”

Figure 3

Linear vs angular motion; the radiated energy is comparable in the two cases.