Quantum toboggans with two branch points

TL;DR

This paper introduces a classification scheme for quantum toboggans with two branch points using winding descriptors and presents a mapping that simplifies their complex contours.

Contribution

It provides a novel classification of QT2 systems and a method to straighten their complex contours through a specific mapping.

Findings

Classification of QT2 via winding descriptors

Mapping that rectifies complex contours for certain cases

Enhanced understanding of wave functions in complex quantum systems

Abstract

Wave functions describing quantum toboggans with two branch points (QT2) are defined along complex contours of coordinates which spiral around these branch points. The classification of QT2 is found in terms of certain ``winding descriptors" $\varrho$. A mapping $x^{(\varrho)}(s) \to y^{(0)}(s)$ is then presented which rectifies the contours for a subset of the simplest $\varrho=\varrho_0$.