On the Schrodinger Operator with a Periodic PT-symmetric Matrix Potential

TL;DR

This paper derives asymptotic formulas for Bloch eigenvalues of a Schrödinger operator with periodic PT-symmetric matrix potential, classifies its spectrum, and identifies conditions for the spectrum to include a half-line.

Contribution

It provides new asymptotic formulas and spectral classification for Schrödinger operators with PT-symmetric periodic matrix potentials, advancing understanding of their spectral properties.

Findings

Asymptotic formulas for Bloch eigenvalues derived

Spectrum classification based on potential coefficients

Condition identified for spectrum to contain a half-line

Abstract

In this article we obtain asymptotic formulas for the Bloch eigenvalues of the operator generated by a system of Schrodinger equations with periodic PT-symmetric complex-valued coefficients. Then using these formulas we classify the spectrum of this operator and find a condition on the coefficients for which the spectrum contains a half line.