The Effect of Impurities on Striped Phases

TL;DR

This paper investigates how localized impurities influence striped phases in one-dimensional systems, developing a mathematical framework to analyze phase and wavenumber changes caused by impurities.

Contribution

It introduces a functional-analytic approach to treat impurity effects on striped phases as a Fredholm problem despite essential spectrum complications.

Findings

Impurities cause jumps in wavenumber and phase depending on their location.

Certain impurity positions lead to no change in wavenumber.

The framework handles essential spectrum issues in the analysis.

Abstract

We study the effect of algebraically localized impurities on striped phases in one space-dimension. We therefore develop a functional-analytic framework which allows us to cast the perturbation problem as a regular Fredholm problem despite the presence of essential spectrum, caused by the soft translational mode. Our results establish the selection of jumps in wavenumber and phase, depending on the location of the impurity and the average wavenumber in the system. We also show that, for select locations, the jump in the wavenumber vanishes.