Reflection coefficient of a reflectionless kink

Abstract

Classically, reflectionless kinks transmit all incident radiation. Recently, we have used an analyticity argument together with a solution of the Lippmann-Schwinger equation to write down the leading quantum correction to the reflection probability. The argument was fast, but rather indirect. In the present paper, we calculate the reflection coefficient and probability by methodically grinding through the Schrödinger picture time evolution. We find the same answer. This answer contains contributions not considered in the traditional calculation of meson-kink scattering in 1991. However, as a result of these contributions, our total result is zero in the case of the Sine-Gordon model, and so it is consistent with integrability. Published by the American Physical Society 2024