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.

21 pages, 12 figures; v2 has improved graphics, more references, minor corrections, two new coauthors

References in corpus (7)

• Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols
• Casimir stress inside planar materials
• Stress tensor for a scalar field in a spatially varying background potential: Divergences, "renormalization," anomalies, and Casimir forces
• Vacuum energy densities of a field in a cavity with a mobile boundary
• Vacuum Casimir energy densities and field divergences at boundaries
• Casimir stress in materials: hard divergency at soft walls
• Torque Anomaly in Quantum Field Theory

Cited by in corpus (12)

• Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium
• Casimir forces in inhomogeneous media: renormalization and the principle of virtual work
• Dynamical Casimir-Polder force between an excited atom and a conducting wall
• Casimir stress in materials: hard divergency at soft walls
• Local Casimir Effect for a Scalar Field in Presence of a Point Impurity
• Renormalization for a Scalar Field in an External Scalar Potential
• Local Neumann semitransparent layers: resummation, pair production and duality
• Vacuum energy density and pressure inside a soft wall
• Disordered Bose-Einstein condensate in hard walls trap
• Vacuum energy, the Casimir effect, and Newton's non-constant
• Scarf for Lifshitz
• Thermodynamics of the scalar radiation in the presence of a reflecting plane wall