Vacuum energy density and pressure near a soft wall

Abstract

Perfectly conducting boundaries, and their Dirichlet counterparts for quantum scalar fields, predict nonintegrable energy densities. A more realistic model with a finite ultraviolet cutoff yields two inconsistent values for the force on a curved or edged boundary (the "pressure anomaly"). A still more realistic, but still easily calculable, model replaces the hard wall by a power-law potential; because it involves no a posteriori modification of the formulas calculated from the theory, this model should be anomaly-free. Here we first set up the formalism and notation for the quantization of a scalar field in the background of a planar soft wall, and we approximate the reduced Green function in perturbative and WKB limits (the latter being appropriate when either the mode frequency or the depth into the wall is sufficiently large). Then we display numerical calculations of energy density and pressure for the region outside the wall, which show that the pressure anomaly does not occur there. Calculations inside the wall are postponed to later papers, which must tackle regularization and renormalization of divergences induced by the potential in the bulk region.

Thermodynamics of the Scalar Radiation in the Presence of a Reflecting Plane Wall

“…[31] for arbitrary N , but the way to obtain them is the same as that leading to eqs. (28) and (29) which appeared first in ref. [31].…”

“…Although equalities have not been included in the bounds of ξ in eqs. (28) to (31) there are evidences that they still hold when equalities are included. Before closing this section it should also be remarked that eqs.…”

“…Such a study has been spoiled by the fact that typically T µν has a nonintegrable divergence at idealized boundaries [14,16], where idealized boundary conditions are assumed to hold in order to model real walls of a cavity. Various proposals to "regularize" such divergences have appeared in the literature [2,17,18,19,20,21,22,23,24,25,26,27] and many aspects of the subject is still actively investigated [28]. The present work wishes to examine further the connections mentioned above.…”

Quantum electromagnetic stress tensor in an inhomogeneous medium

“…In the present paper, inspired by the remarkable results of Ref. [24], we generalize our considerations [25][26][27][28] of the local stress tensor in one-dimensional geometries to the electromagnetic case, in which the role of the potential is played by the permittivity. More precisely, the deviation of the permittivity from its vacuum value will be referred to as the potential in this paper.…”

“…(For more references, see the appendix of Ref. [27], and also Ref. [31], which should have been included there.)…”