Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions

Teo, Lee-Peng

doi:10.1088/1126-6708/2009/11/095

Cited by 28 publications

(27 citation statements)

References 52 publications

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“…[22] (see also Ref. [23] for finite temperature effects), we are able to treat here the more general case of dS spacetime with compact internal subspaces and piston-like geometries. Note that this calculation can be extended to a self-interacting scalar field theory too, in which case mass becomes an effective mass, proportional to the background scalar.…”

Section: Resultsmentioning

confidence: 99%

Casimir effect for parallel plates in de Sitter spacetime

2010

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The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows to explicitly extract the contributions to the expectation values which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power-law (monotonic or oscillating), with independence of the value of the field mass.

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Section: Resultsmentioning

confidence: 99%

Casimir effect for parallel plates in de Sitter spacetime

2010

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“…Extra-dimensional theories with low-energy compactification scale predict Yukawa-type corrections to Newton's gravitational law and the measurements of the Casimir forces between macroscopic bodies provide a sensitive test for constraining the parameters of the corresponding long-range interactions [28][29][30][31][32]. The influence of extra compactified dimensions on the Casimir effect in the classical configuration of two parallel plates has been recently discussed for scalar [33][34][35][36][37][38][39][40], electromagnetic [41][42][43][44][45] and fermionic [46][47][48] fields.…”

Section: Introductionmentioning

confidence: 99%

Casimir effect for scalar current densities in topologically nontrivial spaces

2015

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We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum state becomes unstable. The stability condition depends on the lengths of compact dimensions and is less restrictive than that for background with trivial topology. The vacuum current density is a periodic function of the magnetic flux, enclosed by compact dimensions, with the period equal to the flux quantum. It is explicitly decomposed into the boundary-free and boundary-induced contributions. In sharp contrast to the VEVs of the field squared and the energy-momentum tensor, the current density does not contain surface divergences. Moreover, for Dirichlet condition it vanishes on the boundaries. The normal derivative of the current density on the boundaries vanish for both Dirichlet and Neumann conditions and is nonzero for general Robin conditions. When the separation between the plates is smaller than other length scales, the behavior of the current density is essentially different for non-Neumann and Neumann boundary conditions. In the former case, the total current density in the region between the plates tends to zero. For Neumann boundary condition on both plates, the current density is dominated by the interference part and is inversely proportional to the separation. a

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“…Since then, Casimir effect in the piston setup has attracted considerable interest [37][38][39][40][41][42][43][44][45]. It has also been used to explore the Casimir effect in the presence of extra dimensions [46][47][48][49][50][51][52][53]. Nevertheless, these works either considered scalar fields with Dirichlet or Neumann boundary conditions or more general Robin boundary conditions, or electromagnetic fields with perfect electric conductor conditions or perfect magnetic conductor conditions.…”

Section: Introductionmentioning

confidence: 99%

Casimir piston of real materials and its application to multilayer models

Teo

2010

Phys. Rev. A

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In this article, we derive the formula for the Casimir force acting on a piston made of real material moving inside a perfectly conducting rectangular box. It is shown that by taking suitable limits, one recovers the formula for the Casimir force acting on a perfectly conducting piston or an infinitely permeable piston. The Lifshitz formula for finite temperature Casimir force acting on parallel plates made of real materials is re-derived by considering the five-layer model in the context of the piston approach. It is observed that the divergences of the Casimir force will only cancel under certain conditions, for example, when the regions separated by the plates are filled with media of the same refractive index.

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Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions

Cited by 28 publications

References 52 publications

Casimir effect for parallel plates in de Sitter spacetime

Casimir effect for parallel plates in de Sitter spacetime

Casimir effect for scalar current densities in topologically nontrivial spaces

Casimir piston of real materials and its application to multilayer models

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