# Spectral Walls in Soliton Collisions

## TL;DR

This paper introduces the concept of spectral walls, a nonperturbative spectral change during defect-antidefect scattering, demonstrated in the $$ model with impurity, impacting soliton interactions.

## Contribution

It identifies and analyzes spectral walls as a new phenomenon affecting soliton dynamics, especially in models with internal modes, and isolates this effect using a BPS-preserving impurity.

## Key findings

- Spectral walls cause defect bounce phenomena.
- Spectral walls occur when bound modes merge into the continuum.
- The effect is demonstrated in the $$ model with impurity.

## Abstract

During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the effect can be seen as a hard wall from which the defect can bounce off. We show the existence of these spectral walls and study their properties in the $\phi^4$ model with BPS preserving impurity, where the spectral wall phenomenon can be isolated because the static force between the antikink and the impurity vanishes. We conclude that such spectral walls should surround all solitons possessing internal modes.