Vacuum Energy Density and Pressure Near Boundaries

Fulling, S. A.

doi:10.1142/s0217751x10049645

Cited by 13 publications

(19 citation statements)

References 21 publications

(11 reference statements)

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“…Until such computations are available, it is not meaningful to make a comparison of our results with others, such as those of Barton so similar to those of Ford and Svaiter [37] and Graham and Olum [42,43] as to suggest that all the approaches were on the same track. However, in calculations for a spherical boundary, Martin Schaden and Fulling (unpublished, but summarized in [11]) discovered a pressure anomaly -a violation of Eq. (1.1).…”

Section: Discussionmentioning

confidence: 99%

“…It was reasonable to expect that keeping τ nonzero, and comparable (in natural units) to an interatomic spacing, would yield an effective model of the Casimir effects of a realistic imperfect conductor. However, when ultraviolet regularization is applied to the stress tensor, it produces formulas for energy density and pressure that are inconsistent with each other [11,12]. The principle of virtual work, or energy-pressure balance, requires that a change in the vacuum energy corresponding to some infinitesimal movement of a boundary of the system be attributable to some vacuum pressure pushing against that boundary.…”

Section: Introductionmentioning

confidence: 99%

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Vacuum energy density and pressure near a soft wall

et al. 2016

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vacuum energy density and pressure near a soft wall

et al. 2016

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“…However, recall that the paradox was discovered 6,8 in calculations for a spherical boundary. There also the ultraviolet cutoff gave F = + 1 2 E. But in that case the inside and outside energy layers have the same sign; there is a total energy proportional to surface area, and no cancellation.…”

Section: Curved Hard Wallsmentioning

confidence: 99%

Energy Density and Pressure in Power-Wall Models

Fulling

Milton

Wagner

2012

Int. J. Mod. Phys. Conf. Ser.

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A finite ultraviolet cutoff near a reflecting boundary yields a stress tensor that violates the basic energy-pressure relation. Therefore, a "soft" wall described by a power-law potential, which needs no ad hoc cutoff, is being investigated by the collaboration centered at Texas A&M University and the University of Oklahoma. Progress is reported here.Keywords: vacuum energy; stress tensor; boundary; soft wall. PACS numbers: 03.70.+k, 11.10.Gh Hard Walls: The Pressure Paradox Basic formalism and empty spaceWe model the electromagnetic vacuum-energy problem by a massless scalar field in three space dimensions, subjected to the Dirichlet boundary condition on the "conducting" boundaries. The vacuum energy can be calculated from a Green function, such as the "cylinder kernel", 1,2,3where the φ n are the normalized eigenfunctions with frequencies ω n . The classical formulas for the components of the vacuum expectation value of the stress-energy

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“…By reintroducing dimensionfulh in Eqs. (8) and (10), one sees that the "classical" corrections ρ class and P class carryh 0 whereas the blackbody quantities carry a negative power ofh, namely, h 1−N . Although the terminology "classical" is at some extent justified, by settingh → 0 the "classical" corrections effectively vanish since the blackbody quantities diverge.…”

Section: Some Local Features Of the Hot Radiationmentioning

confidence: 95%

“…Deep in the bulk (x → ∞) ρ class and P class in Eqs. (8) and (10) can be neglected, resulting the usual relations proper of the uniform and isotropic blackbody radiation.…”

Section: Some Local Features Of the Hot Radiationmentioning

confidence: 99%

Hot scalar radiation setting bounds on the curvature coupling parameter

Lorenci

Gomes

Moreira

2015

Class. Quantum Grav.

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This paper addresses the interplay between vacuum and thermal local averages for massless scalar radiation near a plane wall of a large cavity where the Dirichlet boundary condition is assumed to hold. The main result is that stable thermodynamic equilibrium is possible only if the curvature coupling parameter is restricted to a certain range. In more than three spacetime dimensions such a range contains the conformal coupling, but it does not contain the minimal coupling. Since this same range for possible values of the curvature coupling parameter also applies to massive scalar radiation, it may be relevant in settings where arbitrarily coupled scalar fields are present.

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Vacuum Energy Density and Pressure Near Boundaries

Cited by 13 publications

References 21 publications

Vacuum energy density and pressure near a soft wall

Vacuum energy density and pressure near a soft wall

Energy Density and Pressure in Power-Wall Models

Hot scalar radiation setting bounds on the curvature coupling parameter

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