Finite temperature Casimir effect in piston geometry and its classical limit

Abstract

We consider the Casimir force acting on a $d$-dimensional rectangular piston due to massless scalar field with periodic, Dirichlet and Neumann boundary conditions and electromagnetic field with perfect electric conductor and perfect magnetic conductor boundary conditions. It is verified analytically that at any temperature, the Casimir force acting on the piston is always an attractive force pulling the piston towards the interior region, and the magnitude of the force gets larger as the separation $a$ gets smaller. Explicit exact expressions for the Casimir force for small and large plate separations and for low and high temperatures are computed. The limits of the Casimir force acting on the piston when some pairs of transversal plates are large are also derived. An interesting result regarding the influence of temperature is that in contrast to the conventional result that the leading term of the Casimir force acting on a wall of a rectangular cavity at high temperature is the Stefan--Boltzmann (or black body radiation) term which is of order $T^{d+1}$, it is found that the contributions of this term from the interior and exterior regions cancel with each other in the case of piston. The high temperature leading order term of the Casimir force acting on the piston is of order $T$, which shows that the Casimir force has a nontrivial classical $\hslash \to 0$ limit.

References in corpus (23)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Opposites Attract - A Theorem About The Casimir Force
• Improved Precision Measurement of the Casimir Force
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• The Dirichlet Casimir Problem
• Casimir force on a piston
• Attractive Casimir Forces in a Closed Geometry
• Casimir Energies in Light of Quantum Field Theory
• Casimir piston for massless scalar fields in three dimensions
• Casimir Forces in a Piston Geometry at Zero and Finite Temperatures
• Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs
• Comment on the sign of the Casimir force
• Repulsive Casimir Pistons
• Casimir pistons with hybrid boundary conditions
• Thermal Casimir effect in ideal metal rectangular boxes
• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique
• The Casimir force on a piston in the spacetime with extra compactified dimensions
• The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols
• Casimir interaction: pistons and cavity
• One loop boundary effects: techniques and applications
• Casimir energy of two plates inside a cylinder

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