ar X iv : h ep - t h / 05 11 23 6 v 1 2 3 N ov 2 00 5 Dynamical Casimir effect with Robin boundary conditions

We consider a massless scalar field in 1+1 dimensions that satisfies a Robin boundary condition at a non-relativistic moving boundary. Using the perturbative approach introduced by Ford and Vilenkin, we compute the total force on the moving boundary. In contrast to what happens for the Dirichlet and Neumann boundary conditions, in addition to a dissipative part, the force acquires also a dispersive one. Further, we also show that with an appropriate choice for the mechanical frequency of the moving boundary it is possible to turn off the vacuum dissipation almost completely. The interaction between a physical system and a material plate (or cavity in general) in its surroundings has a long history. In 1948, Casimir and Polder [1] computed for the first time the retarded interaction energy between a neutral but polarizable atom and a perfectly conducting wall. At this same year, Casimir [2] predicted the attraction between two neutral parallel conducting plates due to the shift caused by the plates in the energy of the radiation field in vacuum state. Casimir's result may be considered the first problem worked out in detail of the so called cavity QED. Since then, a lot of work has been done on the Casimir effect, see for instance the reviews [3, 4, 5, 6, 7, 8] and references therein (for other phenomena of cavity QED, see [9, 10]). However, the interaction between a quantum field and a material plate is quite complicated. Hence, as a first approximation, it is common to simulate this interaction by imposing an idealized boundary condition on the field. The most familiar conditions are Dirichlet and Neumann ones. A less familiar, but not less important condition is the so called Robin boundary condition, defined for a scalar field by φ| ∂R = β ∂φ ∂n | ∂R , (1) where ∂R is the boundary of the system under study, ∂φ ∂n meansˆn · ∇φ, withˆn being a unitary vector normal to the boundary and β is a parameter with dimension of length