On the finite-zone periodic PT-symmetric potentials

TL;DR

This paper establishes explicit conditions on certain complex-valued periodic potentials to determine when the spectrum of the associated Schrödinger operator has finitely many gaps, advancing understanding of PT-symmetric quantum systems.

Contribution

It provides explicit criteria for the finiteness of spectral gaps in PT-symmetric periodic potentials, a novel contribution to spectral theory in quantum mechanics.

Findings

Derived conditions for finite spectral gaps in PT-symmetric potentials

Characterized spectral properties of complex-valued periodic Schrödinger operators

Enhanced understanding of spectral structure in non-Hermitian quantum systems

Abstract

In this paper we find explicit conditions on the periodic PT-symmetric complex-valued potential q for which the number of gaps in the real part of the spectrum of the one-dimensional Schrodinger operator L(q) is finite.