Pistons modeled by potentials

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.Comment: 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 31

Amplification of the scattering cross section due to non-trivial topology of the spacetime

In previous articles it was demonstrated that the total cross section of the scattering of two light particles (zero modes of the Kaluza-Klein tower) in the six-dimensional $\lambda \phi^{4}$ model differs significantly from the cross section of the same process in the conventional $\lambda \phi^{4}$ theory in four space-time dimensions even for the energies below the threshold of the first heavy particle. Here the analytical structure of the cross section in the same model with torus compactification for arbitrary radii of the two-dimensional torus is studied. Further amplification of the total cross section due to interaction of the scalar field with constant background Abelian gauge potential in the space of extra dimensions is shown.Comment: 23 pages, LaTex, 5 figures available on reques

Finite Temperature Casimir Effect in the Presence of Extra Dimensions

We consider the finite temperature Casimir force acting on two parallel plates in a closed cylinder with the same cross section of arbitrary shape in the presence of extra dimensions. Dirichlet boundary conditions are imposed on one plate and fractional Neumann conditions with order between zero (Dirichlet) and one (Neumann) are imposed on the other plate. Formulas for the Casimir force show that it is always attractive for Dirichlet boundary conditions, and is always repulsive when the fractional order is larger than 1/2. For some fractional orders less than 1/2, the Casimir force can be either attractive or repulsive depending on the size of the internal manifold and temperature.Comment: To appear in the proceedings of 9th Conference on Quantum Field Theory under the Influence of External Conditions (QFEXT 09): Devoted to the Centenary of H. B. G. Casimir, Norman, Oklahoma, 21-25 Sep 200

Scalar Casimir Energies for Separable Coordinate Systems: Application to Semi-transparent Planes in an Annulus

We derive a simplified general expression for the two-body scalar Casimir energy in generalized separable coordinate systems. We apply this technique to the case of radial semi-transparent planes in the annular region between two concentric Dirichlet cylinders. This situation is explored both analytically and numerically.Comment: 8 pages, 5 figures. Contribution to Proceedings of 9th Conference on Quantum Field Theory Under the Influence of External Conditions, QFEXT0

Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions

We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics in a classically chaotic system with multiple scales corresponding to the lengths of the bonds. For graph Laplacians we briefly report results for the spectral determinant, vacuum energy and heat kernel asymptotics of general graphs in terms of the vertex matching conditions.Comment: 5 pages, submitted to proceedings of QFEXT09, minor corrections made