Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions

TL;DR

This paper introduces a solvable 1D quantum well model with nonlocal, non-Hermitian boundary interactions, expanding spectral design possibilities while maintaining unitary evolution through explicit inner product constructions.

Contribution

It presents a new multiparametric PT-symmetric quantum lattice model with nonlocal boundary conditions that remains exactly solvable and allows explicit Hilbert space inner product construction.

Findings

Model exhibits stable, real spectra under nonlocal non-Hermitian boundary conditions.

Exact solutions enable explicit construction of physical inner products.

Enhanced spectral design flexibility compared to local boundary models.

Abstract

Discrete multiparametric 1D quantum well with PT-symmetric long-range boundary conditions is proposed and studied. As a nonlocal descendant of the square well families endowed with Dirac (i.e., Hermitian) and with complex Robin (i.e., non-Hermitian but still local) boundary conditions, the model is shown characterized by the survival of solvability in combination with an enhanced spectral-design flexibility. The solvability incorporates also the feasibility of closed-form constructions of the physical Hilbert-space inner products rendering the time-evolution unitary.