Repulsive Casimir Force

Abstract

The Casimir force between two parallel thick plates, one perfectly dielectric, the other purely magnetic, has been calculated long ago by Boyer [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. Its most characteristic property is that it is repulsive. The problem is actually delicate and counterintuitive, since it implies, for instance, that in the boundary layer of the electric plate the square $E^2$ of the electric field becomes a negative quantity. In the present paper we analyze the problem by first considering the simple harmonic oscillator model introduced by us earlier [J. S. Høye {\it et al.}, Phys. Rev. E {\bf 67}, 056116 (2003); Phys. Rev. A {\bf 94}, 032113 (2016)]. Extension of this model shows how the repulsive behavior can be understood on a microscopic basis, due to the duality between canonical and mechanical momenta in presence of the electromagnetic vector potential. This duality corresponds to the TM and TE modes in electrodynamics. We analyze the generalized Boyer case where the permittivities and permeabilities of the parallel plates are arbitrary. In this respect we first find the induced interaction between a pair of particles with given electric and magnetic polarizabilities and then find it for a pair of parallel plates. The method used for our evaluations is the statistical mechanical one that we have introduced and applied earlier. Whether the pair of particles or plates attract or repel each other depends on their polarizabilities or permittivities and permeabilities respectively. For equal particles or equal plates there is always attraction.

arXiv comment18 pages, no figures

References in corpus (7)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Measurement of the Casimir force between parallel metallic surfaces
• Repulsive Casimir forces
• Does the Transverse Electric Zero Mode Contribute to the Casimir Effect for a Metal?
• Retardation turns the van der Waals attraction into Casimir repulsion already at 3 nm
• Repulsive vacuum-induced forces on a magnetic particle
• Presence of negative entropies in Casimir interactions

Cited by in corpus (11)

• The Free Electron Gas in Cavity Quantum Electrodynamics
• The Casimir effect in topological matter
• Remarks on the Casimir force for magnetodielectric media
• Casimir force between ideal metal plates in a chiral vacuum
• Casimir Friction Between a Magnetic and a Dielectric Material, in the Nonretarded Limit
• Sign inversion in the lateral van der Waals force
• Spontaneous emission of a quantum emitter near a Chern insulator: interplay of time reversal symmetry breaking and van Hove singularity
• Vacuum energy, the Casimir effect, and Newton's non-constant
• On the Axion Electrodynamics in a two-dimensional slab and the Casimir effect
• Quasiperiodic arrangement of magnetodielectric $\delta$-plates: Green's functions and Casimir energies for $N$ bodies
• Casimir energy for $N$ constant conductivity $\delta$-plates with a neural network perception