(Anti-)Stokes Scattering on the Domain Wall String

TL;DR

This paper investigates quantum scattering processes involving a domain wall string in a (2+1)-dimensional scalar field model, focusing on Stokes and anti-Stokes scattering and their probabilities.

Contribution

It provides the first quantum field theory calculation of scattering probabilities involving internal shape modes of domain wall strings, including transmission and reflection cases.

Findings

Derived finite-dimensional integral expressions for scattering probabilities.

Numerical results presented for the $$ double-well model.

Analyzed how incident momenta and angles affect scattering outcomes.

Abstract

In a general (2+1)-dimensional scalar model, we consider the scattering of a single quantum of radiation off a domain wall string, which excites or de-excites the wall's internal shape mode. We refer to these two process as Stokes and anti-Stokes scattering. We calculate the probability densities for these processes to first order in quantum field theory, as a function of incoming momenta and angles. We include both the case in which the incident particle is transmitted and also that in which it bounces backward. Our results are given as finite-dimensional integrals of normal modes and elementary functions, and numerical results are presented in the particular case of the $\phi^4$ double-well model.