Repulsive Casimir Force from Fractional Neumann Boundary Conditions

Abstract

This paper studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a $d$-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.

9 pages, 3 figures

References in corpus (10)

• Casimir force on a piston
• Casimir interaction of two plates inside a cylinder
• Casimir piston for massless scalar fields in three dimensions
• Casimir pistons with hybrid boundary conditions
• Kaluza-Klein models as pistons
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• Comment on: "The Casimir force on a piston in the spacetime with extra compactified dimensions" [Phys. Lett. B 668 (2008) 72]
• Finite temperature Casimir effect in piston geometry and its classical limit
• Topological symmetry breaking of self--interacting fractional Klein--Gordon field on toroidal spacetime
• Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion