Scattering along a complex loop in a solvable PT-symmetric model

TL;DR

This paper investigates a solvable PT-symmetric quantum scattering model with complex paths, revealing how topological features influence reflection and transmission, and linking unitarity points to quantum-knot bound states.

Contribution

It introduces an exactly solvable non-unitary scattering model with complex coordinate paths, demonstrating topological effects on scattering properties and their relation to bound states.

Findings

Reflection and transmission depend on the path topology.

Unitarity points correlate with quantum-knot bound states.

The model is asymptotically local despite complex paths.

Abstract

A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real angular-momentum-like parameter the reflection R and transmission T are shown to change with the winding number (i.e., topology) of the path. The points of unitarity appear related to the points of existence of quantum-knot bound states.