Abstract
We study the zero and finite temperature Casimir force acting on a perfectly conducting piston with arbitrary cross section moving inside a closed cylinder with infinitely permeable walls. We show that at any temperature, the Casimir force always tends to move the piston away from the walls and toward its equilibrium position. In the case of a rectangular piston, exact expressions for the Casimir force are derived. In the high-temperature regime, we show that the leading term of the Casimir force is linear in temperature and therefore the Casimir force has a classical limit. Due to duality, all these results also hold for an infinitely permeable piston moving inside a closed cylinder with perfectly conducting walls.
Highlights
It is well known that the vacuum fluctuations of electromagnetic fields in the presence of boundaries give rise to Casimir force, which was shown to be attractive when the boundary consists of a pair of perfectly conducting parallel plates [1]
He showed that for a 2-dimensional rectangular piston, the Casimir force acting on the piston due to fluctuations of a scalar field with Dirichlet boundary conditions is finite without renormalization and can be computed exactly
We have shown that for a perfectly conducting piston moving freely inside a cylinder with infinitely permeable walls, the Casimir force acting on the piston is a repulsive force which tends to push the piston to its equilibrium position
Summary
It is well known that the vacuum fluctuations of electromagnetic fields in the presence of boundaries give rise to Casimir force, which was shown to be attractive when the boundary consists of a pair of perfectly conducting parallel plates [1]. Even for geometric configuration as simple as a rectangular cavity, despite zeta regularization technique or dimensional regularization method can give finite results for the Casimir force acting on a wall [2, 3], some authors considered these regularization methods which renormalize all surface divergence terms to zero as being not physical [4]. Geyer, Klimchitskaya and Mostepanenko [5] have recently developed a subtraction scheme to obtain a physically consistent Casimir force acting on a wall of a perfectly conducting rectangular cavity from the point of view of thermodynamics. Another approach to this problem was considered by Fulling et al [6].
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