Derivative expansion for the electromagnetic and Neumann-Casimir effects in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>dimensions with imperfect mirrors

Fosco, C. D.; Lombardo, Fernando C.; Mazzitelli, Francisco D.

doi:10.1103/physrevd.91.105019

Cited by 3 publications

(10 citation statements)

References 17 publications

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“…It then satisfies perfect conductor boundary conditions. We have shown this to be equivalent to a real scalar field with Neumann conditions [6], corresponding to the transverse electric (TE) EM mode.…”

Section: Free Energy For the Electromagnetic Fieldmentioning

confidence: 99%

Casimir free energy at high temperatures: Grounded versus isolated conductors

2016

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We evaluate the difference between the Casimir free energies corresponding to either grounded or isolated perfect conductors, at high temperatures. We show that a general and simple expression for that difference can be given, in terms of the electrostatic capacitance matrix for the system of conductors. For the case of close conductors, we provide approximate expressions for that difference, by evaluating the capacitance matrix using the proximity force approximation.Since the high-temperature limit for the Casimir free energy for a medium described by a frequency-dependent conductivity diverging at zero frequency coincides with that of an isolated conductor, our results may shed light on the corrections to the Casimir force in the presence of real materials.

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Section: Free Energy For the Electromagnetic Fieldmentioning

confidence: 99%

Casimir free energy at high temperatures: Grounded versus isolated conductors

2016

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“…But we have shown this to be equivalent to a real scalar field with Neumann conditions [12]. Therefore, this is a Neumann mode, corresponding to the transverse electric (TE) EM mode.…”

Section: Results For the Zero Mode Free Energiesmentioning

confidence: 99%

“…This also holds true for a real scalar field with Neumann conditions in 2+1 dimensions, albeit it can be shown that the non-analyticity can be cured (in a concrete model) by introducing a small departure from perfect Neumann conditions [12].…”

Section: Introductionmentioning

confidence: 99%

“…In order to evaluate the functional integral, we apply a result we obtained in a previous paper [12], whereby we have shown that the calculation of the effective action for a gauge field in the presence of imperfect mirrors could be mapped to a scalar field model. Indeed, using the duality…”

Section: B the Vector Zero-mode Contribution F V (ψ)mentioning

confidence: 99%

“…In this article, we analyse the emergence of non-analyticities in the DE for real materials which, based on the insight from our previous work [12], should come from contributions due to the dimensionally reduced massless modes, which appear as the zero frequency terms in a Matsubara expansion of the fields. To carry out such an analysis, it is convenient to have a general formula for the DE, corresponding to the free energy for the EM field in the presence of media with realistic properties.…”

Section: Introductionmentioning

confidence: 99%

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Derivative expansion for the electromagnetic Casimir free energy at high temperatures

2015

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We study the contribution of the thermal zero modes to the Casimir free energy, in the case of a fluctuating electromagnetic (EM) field in the presence of real materials described by frequencydependent, local and isotropic permittivity ( ) and permeability (µ) functions.Those zero modes, present at any finite temperature, become dominant at high temperatures, since the theory is dimensionally reduced. Our work, within the context of the Derivative Expansion (DE) approach, focusses on the emergence of non analyticities in that dimensionally reduced theory.We conclude that the DE is well defined whenever the function Ω(ω), defined by [Ω(ω)] 2 ≡ ω 2 (ω), vanishes in the zero-frequency limit, for at least one of the two material media involved.

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Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

Fosco,

Lombardo,

Mazzitelli

2024

Physics

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We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different particular geometries, boundary conditions, types of fields, and quantum and thermal fluctuations. Besides providing various examples where the method can be applied, we discuss a concrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditions in 2+1 dimensions. By the same example, we show how a more realistic type of boundary condition circumvents the problem. We also comment on the application of the DE to the Casimir–Polder interaction which provides a broader perspective on particle–surface interactions.

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Derivative expansion for the electromagnetic and Neumann-Casimir effects in2+1dimensions with imperfect mirrors

Cited by 3 publications

References 17 publications

Casimir free energy at high temperatures: Grounded versus isolated conductors

Casimir free energy at high temperatures: Grounded versus isolated conductors

Derivative expansion for the electromagnetic Casimir free energy at high temperatures

Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

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