Casimir interactions between two short-range Coulomb sources

Abstract

We calculate the Casimir interaction between two short range extended charge sources, embedded in a background of one dimensional massive Dirac fermions. We explore both the induced polarization density ρvac(x) and the corresponding integral charge Qvac, as well as the Casimir energy Evac and its contribution to the interaction between sources. For sources with the same charge, by means of the novel ln[Wronskian] contour integration techniques we find that the interaction energy between two sources can exceed sufficiently large negative values and simultaneously reveal the features of a long-range force in spite of non-zero fermion mass, which could significantly influence the properties of such quasi-one-dimensional systems. For large distances between sources we recover that their mutual interaction is governed first of all by the structure of the discrete spectrum of a single source, in dependence on which it can be tuned to give an attractive, a repulsive, or an (almost) compensated Casimir force with various rates of the exponential fall-down, quite different from the standard exp(−2ms) law.