Two-field models in the presence of impurities

TL;DR

This paper explores how impurities affect two-field scalar models, revealing new solutions, altered behaviors, and enhanced flexibility in energy minimization, with implications for physical applications involving inhomogeneities.

Contribution

It demonstrates that impurities can preserve some BPS sectors while significantly modifying solution structures and boundary conditions in two-field models.

Findings

Impurities can change the asymptotic behavior of solutions.

Impurities lead to the emergence of zero-modes and new topological sectors.

Stable, nontrivial configurations can arise from trivial boundary conditions.

Abstract

This work deals with systems of two real scalar fields coupled to impurity functions, meant to model inhomogeneities often encountered in real physical applications. We investigate the theoretical properties of these systems and some of the consequences of impurity doping. We show that the theory may be modified in a way that preserves some BPS sectors, while also greatly impacting the behavior and internal structure of the solution, and exemplify those results with an investigation of a few interesting models in which impurities are coupled to a theory with a quartic potential. It is shown that, in the presence of impurities, the asymptotic behavior of field configurations may be changed, leading to solutions with different long-range properties, which are relevant to several physical applications. Our examples also highlight other important consequences that may follow from the addition of impurities, such as the presence of zero-modes that can significantly change the internal structure of a given solution without altering its energy, the creation of new topological sectors that did not exist in the impurity-free theory, and the possibility of stable, nontrivial configurations generated by topologically trivial boundary conditions. We have also shown that it is sometimes possible to find energy minimizers in BPS sectors which were unpopulated in the canonical theory. These features show that impurities allow for significant flexibility in both the form of energy minimizers and the boundary conditions used to generate them, which may potentially broaden the range of applicability of the theory.