Pistons modeled by potentials

Abstract

In this article we consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration. In order to compute the determinant and Casimir force we employ the zeta function scheme. Essentially, the computation reduces to the analysis of the zeta function associated with a scalar field living on an interval $[0,L]$ in a background potential. Although, as a model for a piston, it seems reasonable to assume a potential having compact support within $[0,L]$, we provide a formalism that can be applied to any sufficiently smooth potential.

10 pages, LaTeX. A typo in eq. (3.5) has been corrected. In "Cosmology, Quantum Vacuum and Zeta Functions: In Honour of Emilio Elizalde", Eds. S.D. Odintsov, D. Saez-Gomez, and S. Xambo-Descamps. (Springer 2011) pp 313

References in corpus (4)

• Casimir force on a piston
• Casimir interaction of two plates inside a cylinder
• Kaluza-Klein models as pistons
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime

Cited by in corpus (11)

• Two-point one-dimensional $\delta$-${\delta }^{\prime }$ interactions: non-abelian addition law and decoupling limit
• Casimir Effect in the Presence of External Fields
• Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem
• Spectral determinants and zeta functions of Schrödinger operators on metric graphs
• The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type $I{\times }_{f}N$
• Hyperspherical $\delta \text{-}{\delta }^{\prime }$ potentials
• The Casimir Effect for Generalized Piston Geometries
• Casimir pistons with generalized boundary conditions: a step forward
• Vacuum energy of Schrödinger operators on metric graphs
• The Casimir Effect for Thick Pistons
• Black holes and quantum theory on manifolds with singular potentials