Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint

2025/07/13 by Znojil, Miloslav
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2507.09567

Abstract

A family of discrete Schrödinger equations with imaginary potentials V(x) is studied. Inside the domain \cal D of unitarity-compatible values of V(x), the reality of all of the bound-state energies survives up to the ``exceptional-point'' (EP) maximally non-Hermitian spectral-degeneracy boundaries ∂ \cal D. The computer-assisted localization of the EP limits is performed showing that the complexity of the task grows quickly with the number N of grid points x.

Citations

• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Making sense of non-Hermitian Hamiltonians

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