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arXiv:2504.02082 · Physica A Statistical Mechanics and its Applications

Exact dynamics and Bloch oscillations in a non-Hermitian zigzag Glauber–Fock lattice

G.S. Fahara-Ojeda, L. A. Tapia-Alarcón, Braulio Misael Villegas-Martínez, George K. Thiruvathukal, Antônio Francisco Neto, Sandra Gesing, T. Battelle, Vlado Stankovski, Ivan A. Bocanegra-Garay, Araceli Venegas‐Gomez, Jesus Escobedo-Alatorre, Roberto Alan Beltrán Vargas

Published Jul 18, 2025• 2 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2025.130811

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The effect of a non-unitary transformation on an initial Hermitian operator is studied. The initial (Hermitian) optical system is a Glauber-Fock optical lattice. The resulting non-Hermitian Hamiltonian models an anisotropic (Glauber-Fock) waveguide array of the Hatano-Nelson-type. Several cases are analyzed and exact analytical solutions for both the Hermitian and non-Hermitian Schrödinger problems are given, as they are simply connected. Indeed, such transformation can be regarded as a non-unitary Supersymmetric transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.
The effect of a non-unitary transformation on an initial Hermitian operator is studied. The initial (Hermitian) optical system is a Glauber-Fock optical lattice. The resulting non-Hermitian Hamiltonian models an anisotropic (Glauber-Fock) waveguide array of the Hatano-Nelson-type. Several cases are analyzed and exact analytical solutions for both the Hermitian and non-Hermitian Schrödinger problems are given, as they are simply connected. Indeed, such transformation can be regarded as a non-unitary Supersymmetric (SUSY) transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.