Casimir Force on a Piston in Randall–Sundrum Models

Cheng, Hongbo

doi:10.1088/0253-6102/53/6/27

Cited by 7 publications

(3 citation statements)

References 61 publications

(61 reference statements)

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“…Using zeta function regularization, the Casimir energy and force have been computed. Explicit results in two-dimensions, equations ( 14) and (22), and three-dimensions, equations (15) and (23), are given, but any dimension can be dealt with in principle. At the center of the technicalities is a WKB analysis of the initial value problem described in equation (4).…”

Section: Discussionmentioning

confidence: 99%

“…Equation (15) gives that for a three-dimensional massless scalar field, the Casimir force is given by…”

Section: ( )mentioning

confidence: 99%

“…A large variety of piston configurations have been studied differing in their cross sections and the boundary conditions imposed. Mostly flat pistons where considered [1,21,25,29,32,34,35,37,39,[43][44][45]48], but also curved pistons have been analyzed [15,16,24,26,42].…”

Section: Introductionmentioning

confidence: 99%

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Casimir effect for smooth potentials on spherically symmetric pistons

Morales-Almazan¹,

Kirsten²

2015

J. Phys. A: Math. Theor.

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Section: Discussionmentioning

confidence: 99%

“…Equation (15) gives that for a three-dimensional massless scalar field, the Casimir force is given by…”

Section: ( )mentioning

confidence: 99%

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Casimir effect for smooth potentials on spherically symmetric pistons

Morales-Almazan¹,

Kirsten²

2015

J. Phys. A: Math. Theor.

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The Casimir effect for conical pistons

Fucci

Kirsten

2011

J. High Energ. Phys.

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In this paper we utilize ζ-function regularization techniques in order to compute the Casimir force for massless scalar fields subject to Dirichlet and Neumann boundary conditions in the setting of the conical piston. The piston geometry is obtained by dividing the bounded generalized cone into two regions separated by its cross section positioned at a with a ∈ (0, b) with b > 0. We obtain expressions for the Casimir force that are valid in any dimension for both Dirichlet and Neumann boundary conditions in terms of the spectral ζ-function of the piston. As a particular case, we specify the piston to be a d-dimensional sphere and present explicit results for d = 2, 3, 4, 5. I. INTRODUCTIONThe Casimir effect is one of the most important macroscopic manifestations of the zero point energy of quantized fields under the influence of external conditions [11,38] or in spaces with non-trivial topology. In recent years, a vast amount of literature has been produced on the Casimir effect, which was first predicted in the seminal paper [13], especially for its relevance in nanoscale physics [10,11,38]. Due to its nature, calculations of the vacuum energy lead to divergencies which need to be regularized and subsequently renormalized. Several regularization methods exist, amongst the most important ones are frequency cutoff, point splitting and zeta function regularization [6,10,12,22,23,38]. For many configurations, these techniques yield the same finite renormalized result, however the way divergencies are removed is different in each scheme. The non-uniqueness of the removal procedure raises the question, which of them is the physically best motivated one. Technical and interpretational problems of this nature can actually be avoided if one considers the Casimir effect between separate objects. In this case, the divergent part of the energy (for massless fields) depends on the heat kernel coefficient a D/2 related to the geometry of the objects.These coefficients, in turn, do not depend on the distance between the bodies and, hence, the Casimir force between them is free of divergencies [10]. Belonging to the class of configurations for which the Casimir force has been unambiguously evaluated are pistons of certain types.These piston configurations, introduced in [14], have become increasingly important because of this fact. A large variety of piston configurations and boundary conditions have been studied throughout the lit- *

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Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

Cheng

2012

Commun. Theor. Phys.

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We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region.We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.

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Casimir Force on a Piston in Randall–Sundrum Models

Cited by 7 publications

References 61 publications

Casimir effect for smooth potentials on spherically symmetric pistons

Casimir effect for smooth potentials on spherically symmetric pistons

The Casimir effect for conical pistons

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

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