Casimir effect as a sum over modes in dissipative systems

Intravaia, Francesco; Behunin, Ryan O.

doi:10.1103/physreva.86.062517

Cited by 35 publications

(45 citation statements)

References 59 publications

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“…The factor det[ P − → (v) (−a)] = e a ν λ ν represents the contribution of the continuum of electromagnetic vacuum modes hitting the gratings [9]. Similarly, the…”

Section: A Two Lamellar Gratingsmentioning

confidence: 99%

“…Recent theoretical developments have shown how to compute the Casimir force between complex structures using a variety of methods [2][3][4][5]. Among these, we mention techniques based on the summation of zero-point energies [6][7][8][9], which are suitable for highsymmetry problems; the scattering approach which requires the computation of the reflection matrices of the scatterers [10][11][12][13]; and full-wave numerical techniques, which compute the force from the Maxwell stress tensor [4,5,14].…”

Section: Introductionmentioning

confidence: 99%

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Quasianalytical modal approach for computing Casimir interactions in periodic nanostructures

et al. 2012

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We present an almost fully analytical technique for computing Casimir interactions between periodic lamellar gratings based on a modal approach. Our method improves on previous work on Casimir modal approaches for nanostructures [Phys. Rev. A 82, 062111 (2010)] by using the exact form of the eigenvectors of such structures, and computing eigenvalues by solving numerically a simple transcendental equation. In some cases eigenvalues can be solved for exactly, such as the zero-frequency limit of gratings modeled by a Drude permittivity. Our technique also allows us to predict analytically the behavior of the Casimir interaction in limiting cases, such as the large-separation asymptotics. The method can be generalized to more complex grating structures and may provide a deeper understanding of the geometry-composition-temperature interplay in Casimir forces between nanostructures.

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“…The factor det[ P − → (v) (−a)] = e a ν λ ν represents the contribution of the continuum of electromagnetic vacuum modes hitting the gratings [9]. Similarly, the…”

Section: A Two Lamellar Gratingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasianalytical modal approach for computing Casimir interactions in periodic nanostructures

et al. 2012

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“…Then, we use a generalization of the matrix determinant lemma on the above expression (see the Appendix). For instance, for the numerator we have according to (27)…”

Section: Determinant Formula For Two Scatterersmentioning

confidence: 99%

“…Among other worries, it has also been suggested that the scattering might not be valid for the dissipative metallic plates used in the experiments [24]. Some works have been devoted to ab initio treatments of the Casimir interaction between dissipative mirrors [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Accounting for Dissipation in the Scattering Approach to the Casimir Energy

et al. 2018

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Abstract:We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account implicitly. We prove that this formula is also valid when the surrounding medium is dissipative.

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“…Despite this, the use of the argument principle using lossy materials still seemingly resulted in the correct Casimir force [8,12,13]. Only recently have papers have been published that rigorously explain why [14][15][16][17].…”

Section: Derivationmentioning

confidence: 99%

Casimir Force for Arbitrary Objects Using the Argument Principle and Boundary Element Methods

Atkins¹,

Dai²,

Sha³

et al. 2013

PIER

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Abstract-Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplified derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.

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Casimir effect as a sum over modes in dissipative systems

Cited by 35 publications

References 59 publications

Quasianalytical modal approach for computing Casimir interactions in periodic nanostructures

Quasianalytical modal approach for computing Casimir interactions in periodic nanostructures

Accounting for Dissipation in the Scattering Approach to the Casimir Energy

Casimir Force for Arbitrary Objects Using the Argument Principle and Boundary Element Methods

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