Casimir energy for a dielectric cylinder

Cavero-Peláez, Inés; Milton, Kimball A.

doi:10.1016/j.aop.2005.05.007

Cited by 61 publications

(74 citation statements)

References 38 publications

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“…For example, keeping none of those corrections, that is setting M = 0, we get for p = 1, e(1) ≈ −0.0010847. Keeping three terms is sufficient to find that e(1) is less than 10 −6 ; indeed, the circular cylinder value is e(1) = 0 [21,22,23,24,25]. This function e(p) is plotted in Fig.…”

Section: Dielectric Boundary At R = Amentioning

confidence: 94%

“…[21] to obtain the weakcoupling Casimir self-energy for a purely dielectric wedge, where µ 1 = µ 2 = 1. We can only examine the coefficient of (ǫ 1 − ǫ 2 ) 2 because the result is divergent in higher orders.…”

Section: Dielectric Boundary At R = Amentioning

confidence: 99%

“…The energy per area in the wedge isẼ (4.25) where the exact form of g m is elaborate, but has the asymptotic form where y = mpz, and f k are rational functions of z, given in Ref. [21], about which all we need to know here is…”

Section: Dielectric Boundary At R = Amentioning

confidence: 99%

“…This applies * Electronic address: iver.h.brevik@ntnu.no † Electronic address: simen.a.ellingsen@ntnu.no ‡ Electronic address: milton@nhn.ou.edu to the case of a perfectly conducting circular boundary [17,18,19,20], as well as to the case of a dielectric circular boundary [21,22,23,24,25]. Another reason for studying the wedge is the analogy-at least in a formal sense-with the theory of a cosmic string (cf., for instance, Ref.…”

Section: Introductionmentioning

confidence: 99%

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Electrodynamic Casimir effect in a medium-filled wedge

2009

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We re-examine the electrodynamic Casimir effect in a wedge defined by two perfect conductors making dihedral angle α = π/p. This system is analogous to the system defined by a cosmic string. We consider the wedge region as filled with an azimuthally symmetric material, with permittivity/permeability ε1, µ1 for distance from the axis r < a, and ε2, µ2 for r > a. The results are closely related to those for a circular-cylindrical geometry, but with non-integer azimuthal quantum number mp. Apart from a zero-mode divergence, which may be removed by choosing periodic boundary conditions on the wedge, and may be made finite if dispersion is included, we obtain finite results for the free energy corresponding to changes in a for the case when the speed of light is the same inside and outside the radius a, and for weak coupling, |ε1 − ε2| ≪ 1, for purely dielectric media. We also consider the radiation produced by the sudden appearance of an infinite cosmic string, situated along the cusp line of the pre-existing wedge.

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Section: Dielectric Boundary At R = Amentioning

confidence: 94%

Section: Dielectric Boundary At R = Amentioning

confidence: 99%

Section: Dielectric Boundary At R = Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electrodynamic Casimir effect in a medium-filled wedge

2009

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“…Although the first two orders in λ identically vanish, a divergence in the energy (14) does occur in O(λ 3 ).…”

Section: Exponential Regulatormentioning

confidence: 98%

Local and Global Casimir Energies in a Green's Function Approach

Milton¹,

Cavero-Peláez²,

Kirsten³

2008

The Eleventh Marcel Grossmann Meeting

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The effects of quantum fluctuations in fields confined by background configurations may be simply and transparently computed using the Green's function approach pioneered by Schwinger. Not only can total energies and surface forces be computed in this way, but local energy densities, and in general, all components of the vacuum expectation value of the energy-momentum tensor may be calculated. For simple geometries this approach may be carried out exactly, which yields insight into what happens in less tractable situations. In this talk I will concentrate on the example of a scalar field in a circular cylindrical delta-function background. This situation is quite similar to that of a spherical delta-function background. The local energy density in these cases diverges as the surface of the background is approached, but these divergences are integrable. The total energy is finite in strong coupling, but in weak coupling a divergence occurs in third order. This universal feature is shown to reflect a divergence in the energy associated with the surface, the integrated local energy density within the shell itself, which surface energy should be removable by a process of renormalization.

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Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

Milton

2011

Casimir Physics

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From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, ∑ 1 2h ω, seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, T 00 , typically diverge near boundaries. These two types of divergences have little to do with each other. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The divergent local energy densities near surfaces do not change when the relative position of the rigid bodies is altered. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The finiteness of self-energies is separate from the issue of the physical observability of the effect. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein's equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle. This should be a general property, but has not yet been established, for 1 2 Kimball A. Milton example, for the Boyer sphere. It is known that such local divergences can have no effect on macroscopic causality.

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Casimir energy for a dielectric cylinder

Cited by 61 publications

References 38 publications

Electrodynamic Casimir effect in a medium-filled wedge

Electrodynamic Casimir effect in a medium-filled wedge

Local and Global Casimir Energies in a Green's Function Approach

Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

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