Surprises in Theoretical Casimir Physics by William M. R. Simpson

Author:William M. R. Simpson
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.2.1)

Are the divergent terms in the ground-state energy still independent of ? We will imagine this medium as a rigid body, so that we can neglect any energy associated with deformation, and attempt to find the behaviour of the force necessary to hold the mirror fixed at by computing the mechanical energy of the system. Let us begin by considering the particular case illustrated in Fig. 4.1,

(4.2.2)

where the inhomogeneity is written as , and is a small parameter describing the size of the perturbation. We emphasise that we are considering some arbitrary fixed value of . The quantity only occurs in this expression in order to make the permittivity equal to that of free space at the edges of the cavity.

Fig. 4.1As in Fig. 1.​2, we consider a perfectly reflecting rectangular chamber of length and cross sectional area, . Within the chamber is a mirror, positioned at , and surrounded by an inhomogeneous dielectric with and given by (4.2.1). We seek the dependence of the energy of this system on the parameter

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