Casimir force between vortex matter in anisotropic and layered superconductors

We present an approach to calculate the attractive long-range vortex-vortex interaction of the van der Waals type present in anisotropic and layered s uperconductors. The mapping of the statistical mechanics of vortex lines on to the imaginary time quantum mechanics of two-dimensional charged bosons a llows us to define a two-dimensional (2D) Casimir problem: Two half spaces of (dilute) vortex matter separated by a gap of width R are mapped to two d ielectric half planes of charged bosons interacting via a massive gauge fie ld. We determine the attractive Casimir force between the two half planes a nd show that it agrees with the pairwise summation of the van der Waals for ce between vortices previously found by Blatter and Geshkenbein [Phys. Rev. Leu. 77, 4958 (1996)]. [S0163-1829(99)01818-4].