Resumo

BOCANEGRA-GARAY, I. A.  e  MOYA-CESSA, H. M.. Non-Hermitian transport in Glauber-Fock optical lattices. Rev. mex. fis. [online]. 2024, vol.70, n.4, e041303.  Epub 12-Set-2025. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.70.041303.

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.

Palavras-chave : Glauber-Fock waveguide array; non-unitary transformation; non-hermitian hamiltonians.

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