Casimir Interactions between Magnetic Flux Tubes in a Dense Lattice

Understand

We use the worldline numerics technique to study a cylindrically symmetric model of magnetic flux tubes in a dense lattice and the non-local Casimir forces acting between regions of magnetic flux.

• Within a superconductor the magnetic field is constrained within magnetic flux tubes and if the background magnetic field is on the order the quantum critical field strength, $B_k = \frac{m^2}{e} = 4.4 \times 10^{13}$ Gauss, the magnetic field is likely to vary rapidly on the scales where \acs{QED} effects are important.
• In this paper, we construct a cylindrically symmetric toy model of a flux tube lattice in which the non-local influence of \acs{QED} on neighbouring flux tubes is taken into account.
• We compute the effective action densities using the worldline numerics technique.