Impurity-doped scalar fields in arbitrary dimensions

Abstract

We investigate the presence of localized structures for relativistic scalar fields coupled to impurities in arbitrary spatial dimensions. Such systems present spatial inhomogeneity, realized through the inclusion of explicit coordinate dependence in the Lagrangian. It is shown that, in stark contrast to the impurity-free scenario, Derrick's argument does not present a strong hindrance to the existence of stable solutions in this case. Bogomol'nyi equations giving rise to global minima of the energy are found, and some of the ensuing BPS configurations are presented.