Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors

Abstract

We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of non-magnetic materials (Guérout et al, Phys. Rev. E 90 042125), we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.

Comment on “Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors”

“…It should be noted, however, that the redefined plasma model (2) introduced in Ref. [8] also does not match the optical and electrical properties of gold. As recognized in Ref.…”

“…As stated in Ref. [8], "The lossless plasma model, with susceptibility χ 0 (ω), does not match the optical and electrical properties of gold, and it cannot describe correctly the Casimir pressure between two metallic plates." According to Ref.…”

“…Reference [8] discusses this puzzle and arrives at a conclusion that the lossless plasma model which is commonly used has to be redefined as the limit of the Drude model…”

“…In other words, the Drude model (1) is a discontinuous function of γ at the point γ = 0, and Ref. [8] favors the definition of the plasma model by Eq. (2) over that of Eq.…”

“…According to Ref. [8], "the plasma model can only be considered as an effective model at high frequencies ω ≫ γ. Considered in this manner, it has to be defined as the limit of the Drude model when γ → 0", i.e., by Eq.…”