Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media

Abstract

The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situation. We also discuss the appropriate choice of the electromagnetic energy-momentum tensor.

Analytical and numerical demonstration of how the Drude dispersive model satisfies Nernst's theorem for the Casimir entropy

“…A sketch of the setup is given in figure 1. The present work is closely related to our recent paper [1] in particular, and also to our earlier papers on the thermal Casimir effect [2][3][4][5][6].…”

“…As mentioned, the only place where there is a need to use the Drude relation (3) explicitly is when m = 0. Actually, it is immaterial whether we use the experimental Lambrecht data (5) or the Drude relation directly.…”

Recent developments in the Casimir effect

“…However, we [12] and others have shown that for real metals, where γ has a residual value at zero temperature, the free energy per area has a vanishing slope at the origin. Indeed, in the Drude model, the free energy per area has the behavior [13,14] …”

Casimir energy and entropy between dissipative mirrors

“…Step (i) was essentially achieved by Lifshitz in 1955 [7], and within the same theory, addressing step (ii) was apparently trivial. Surprisingly, up to now, the role of dissipation in the temperature correction to the force between two dissipative metallic slabs is unclear and at the center of hottest controversy around the Casimir effect [8][9][10][11][12][13][14][15]. Lifshitz adopts a 'matter' point of view to calculate the Casimir effect building on a stochastic (Langevin) version of the Maxwell equations where quantum fluctuating currents are responsible for the fields.…”