Spherical Casimir pistons

J S Dowker (1)

1 School of Physics and Astronomy [Manchester]

A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta-function regularisation, the vacuum energy of the arrangement is finite for conformal propagation in space-time. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is repelled or attracted by the nearest wall if d = 3, 7,... or if d = 1, 5,..., respectively. For hybrid N − D conditions these requirements are switched. If a mass is added, divergences arise which render the model suspect. The analysis, however, is relatively straightforward and involves the Barnes zeta function. The extension to finite temperatures is made and it is shown that for the 3, 7,... series of odd spheres, the repulsion by the walls continues but that, above a certain temperature, the free energy acquires two minima symmetrically placed about the mid point.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

J S Dowker. Spherical Casimir pistons. Classical and Quantum Gravity, 2011, 28 (15), pp.155018. ⟨10.1088/0264-9381/28/15/155018⟩. ⟨hal-00723009⟩