Numerical Methods for Computing Casimir Interactions

Johnson, Steven G.

doi:10.1007/978-3-642-20288-9_6

Cited by 35 publications

(50 citation statements)

References 129 publications

(291 reference statements)

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“…Furthermore, we can obtain the nondegenerate orthogonality conditions as (19) Similar to the original problem, the degenerate curl-free modes of the auxiliary system satisfy where are eigensolutions of (20) and (21) for lossy and non-reciprocal problems, respectively. Again, for , we have (22) For other degenerate cases, we can also apply the Gram-Schmit orthogonalization process.…”

Section: A Bounded Casementioning

confidence: 98%

See 1 more Smart Citation

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Dai¹,

Lo²,

Chew

et al. 2014

IEEE Trans. Antennas Propagat.

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A generalized modal expansion theory for investigating arbitrary 3-D bounded and unbounded electromagnetic fields is presented. When an inhomogeneity is enclosed with impenetrable boundaries, the field excited by arbitrary sources is expanded with a complete set of eigenmodes, which are classified into trapped modes and radiation modes. As the boundaries tend to infinity, trapped modes remain unchanged, while radiation modes form a continuum. To illustrate the theory, several real-life structures are investigated with a conformal finite-difference technique in the frequency domain. Perfectly matched layers (PMLs) are imposed at finite extent to emulate the unbounded problems. Numerical examples show that, only a few system modes are prominent in expanding an excited field, leading to a reduced modal picture which provides a quick guidance as well as useful physical insight for engineering design and optimization of electromagnetic devices and components.

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Section: A Bounded Casementioning

confidence: 98%

“…Recent research has extended to metamaterial-inspired devices, including photonic band-gap (PBG)-based optical guides and resonators [11]- [14]. Moreover, modal analysis may find applications in nanoelectromechanical systems (NEMS) related problems, where the Casimir effect needs to be accounted for [20].…”

Section: Introductionmentioning

confidence: 99%

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Dai¹,

Lo²,

Chew

et al. 2014

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

show abstract

“…Moreover, even in a free field theory the Casimir problem cannot be solved exactly for a physical object of an arbitrary shape. Therefore the Casimir effect is often studied using certain analytical approximations such as the proximity-force approximation [6] as well as utilizing numerical tools [7] which includes worldline approaches [8] and methods of lattice field theories [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Casimir effect and deconfinement phase transition

2017

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We show that the Casimir effect may lead to a deconfinement phase transition induced by the presence of boundaries in confining gauge theories. Using first-principle numerical simulations we demonstrate this phenomenon in the simplest case of the compact lattice electrodynamics in two spatial dimensions. We find that the critical temperature of the deconfinement transition in the vacuum between two parallel dielectric/metallic wires is a monotonically increasing function of the separation between the wires. At infinite separation the wires do not affect the critical temperature while at small separations the vacuum between the wires looses the confinement property due to modification of vacuum fluctuations of virtual monopoles.

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“…These forces may be either attractive or repulsive depending on geometrical shape of the conductors. There are various numerical tools to compute Casimir interactions [5] including worldline Monte-Carlo methods [6,7].…”

Section: Introductionmentioning

confidence: 99%

Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions

2016

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We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.

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Numerical Methods for Computing Casimir Interactions

Cited by 35 publications

References 129 publications

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Casimir effect and deconfinement phase transition

Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions

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