Some aspects of jump-defects in the quantum sine-Gordon model

TL;DR

This paper investigates how classical jump-defects in the sine-Gordon model translate to the quantum case, revealing stable and unstable defect types, their scattering behaviors, and unique transmission properties of breathers.

Contribution

It extends the classical jump-defect concept to the quantum sine-Gordon model, analyzing defect types, scattering processes, and unique breather transmission characteristics.

Findings

Two defect types: stable even charge and unstable odd charge.

Jump-defects are purely transmitting in quantum scattering.

Lightest breather's transmission is independent of bulk coupling.

Abstract

The classical sine-Gordon model permits integrable discontinuities, or jump-defects, where the conditions relating the fields on either side of a defect are Backlund transformations frozen at the defect location. The purpose of this article is to explore the extent to which this idea may be extended to the quantum sine-Gordon model and how the striking features of the classical model may translate to the quantum version. Assuming a positive defect parameter there are two types of defect. One type, carrying even charge, is stable, but the other type, carrying odd charge, is unstable and may be considered as a resonant bound state of a soliton and a stable defect. The scattering of solitons with defects is considered in detail, as is the scattering of breathers, and in all cases the jump-defect is purely transmitting. One surprising discovery concerns the lightest breather. Its transmission factor is independent of the bulk coupling - a property susceptible to a perturbative check, but not shared with any of the other breathers. It is argued that classical jump-defects can move and some comments are made concerning their quantum scattering matrix.