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 (24)

• Fractional Schrodinger equation
• Spectral Dimension of the Universe
• Time fractional Schrodinger equation
• Reconstructing the Universe
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Casimir force on a piston
• Casimir interaction of two plates inside a cylinder
• Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons
• Casimir piston for massless scalar fields in three dimensions
• Casimir pistons with hybrid boundary conditions
• Kaluza-Klein models as pistons
• On bosonization in $3$ dimensions
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• Running Coupling Constants, Newtonian Potential and non localities in the Effective Action
• Relativistic wave equations with fractional derivatives and pseudo-differential operators
• Canonical quantization of non-local field equations
• Compact dimensions and the Casimir effect: the Proca connection
• 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
• Cubic root of Klein-Gordon equation
• Finite Temperature Casimir Effect for a Massless Fractional Klein-Gordon field with Fractional Neumann Conditions
• Topological symmetry breaking of self--interacting fractional Klein--Gordon field on toroidal spacetime
• Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion
• Fractal Propagators in QED and QCD and Implications for the Problem of Confinement

Cited by in corpus (10)

• q-deformed Lie algebras and fractional calculus
• Common aspects of q-deformed Lie algebras and fractional calculus
• Casimir Effect under Quasi-Periodic Boundary Condition Inspired by Nanotubes
• Casimir effect with a helix torus boundary condition
• One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law
• The Casimir Energy For Scalar Field With Mixed Boundary Condition
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Finite Temperature Casimir Effect in the Presence of Extra Dimensions
• A spectral penalty method for two-sided fractional differential equations with general boundary conditions
• Generalized Quantum Spring