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Register a new userCasimir-Lifshitz pressure on cavity walls
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Authors
C. Romaniega
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We extend our previous work on the electromagnetic Casimir-Lifshitz interaction between two bodies when one is contained within the other. We focus on the fluctuation-induced pressure acting on the cavity wall, which is assumed to be spherical. This pressure can be positive or negative depending on the response functions describing the bodies and the medium filling the cavity. However, we find that, under general hypotheses, the sign is independent of the geometry of the configuration. This result is based on the representation of the Casimir-Lifshitz energy in terms of transition operators. In particular, we study the components of these operators related to inside scattering amplitudes, adapting the invariant imbedding procedure to this unfamiliar scattering setup. We find that our main result is in agreement with the Dzyaloshinskii-Lifshitz-Pitaevskii result, which is obtained as a limiting case.
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We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii-Lifshitz-Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir-Lifshitz forces, the result is based on the scattering formalism. In this case the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the self-energy contribution to the pressure tend to expand the sphere.
The zero-temperature Casimir-Lifshitz force between two plates moving parallel to each other at arbitrary constant speed was found in [New J. Phys. 11, 033035 (2009)]. The solution is here generalized to the case where the plates are at different temperatures. The Casimir-Lifshitz force is obtained by calculating the electromagnetic stress tensor, using the method employed by Antezza et al. [Phys. Rev. A 77, 022901 (2008)] for non-moving plates at different temperatures. The perpendicular force on the plates has contributions from the quantum vacuum and from the thermal radiation; both of these contributions are influenced by the motion. In addition to the perpendicular force, thermal radiation from the moving plates gives rise to a lateral component of the Casimir-Lifshitz force, an effect with no quantum-vacuum contribution. The zero-temperature results are reproduced, in particular the non-existence of a quantum-vacuum friction between the plates.
The Casimir force and free energy at low temperatures has been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is new. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the analytic results.
The controversy concerning the temperature correction to the Casimir force has been ongoing for almost a decade with no view to a solution and has recently been extended to include semiconducting materials. We review some theoretical aspects of formal violations of Nernsts heat theorem in the context of Casimir Lifshitz thermodynamics and the role of the exponent of the leading term of the dielectric permittivity with respect to imaginary frequency. A general formalism for calculating the temperature corrections to free energy at low temperatures is developed for systems which do not exhibit such anomalies, and the low temperature behaviour of the free energy in a gap between half-spaces of poorly conducting materials modelled with a Drude type permittivity is calculated.
We show that the claims expressed in the Comment arXiv:0810.3244v1 by R.S. Decca et al against our paper, D.A.R. Dalvit and S.K. Lamoreaux, Phys. Rev. Lett. {bf 101}, 163203 (2008), are wrong and manifestly inconsistent with basic principles of statistical physics.
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