PT-symmetric knotting of coordinates: a new, topological mechanism of quantum confinement

TL;DR

This paper introduces a novel topological quantum confinement mechanism using PT-symmetric knotting of complex coordinates, leading to exactly solvable bound states without traditional potentials.

Contribution

It presents the first exactly solvable PT-symmetric model where bound states arise purely from topological properties of complex coordinate contours.

Findings

Bound states exist without confining potentials.

States are topologically protected by complex coordinate contours.

Model is exactly solvable and demonstrates new quantum confinement mechanism.

Abstract

We construct an exactly solvable PT-symmetric example of Sturmian bound states which exist in the absence of any confining potential. Their origin is purely topological -- these states live on certain nontrivial contours of complex coordinates.