2010 **Abstract:** We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of…

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“…Clearly, this is equivalent to solving a scattering problem at real frequencyω with materials ε(x) = ε(x)(1 + i/2Q) andμ(x) = µ(x)(1 + i/2Q). (In fact, any change to the frequency can be converted into a change of materials [50].) In particular, adding a positive imaginary part to ω (forω k in the upper-half plane [11]) corresponds to a positive imaginary part inε(x) and µ(x), which corresponds (with our e −iωt convention) to an absorption loss.…”

confidence: 99%

“…Clearly, this is equivalent to solving a scattering problem at real frequencyω with materials ε(x) = ε(x)(1 + i/2Q) andμ(x) = µ(x)(1 + i/2Q). (In fact, any change to the frequency can be converted into a change of materials [50].) In particular, adding a positive imaginary part to ω (forω k in the upper-half plane [11]) corresponds to a positive imaginary part inε(x) and µ(x), which corresponds (with our e −iωt convention) to an absorption loss.…”

confidence: 99%

“…Practical applications are likely to explore geometries further removed from parallel plates. Several numerical schemes (14, -16), and even an analog computer (17), have recently been developed for computing Casimir forces in general geometries. However, analytical formulae for quick and reliable estimates remain highly desirable.…”

mentioning

confidence: 99%

“…[13,27]. More generally, this equivalence between the Casimir force and a relatively narrowbandwidth real-frequency response of a dissipative system potentially opens other avenues for the understanding of Casimir physics [120].…”

confidence: 82%

“…ω = iξ for a Wick rotation). Equivalently, we can view this as a calculation at a real frequency ξ for a transformed complex material : ω 2 ε(ω, x) → ξ 2 ε c (ξ, x) where the transformed material is [13,120]…”

confidence: 99%