A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators

Abstract

We show how, given a non-Hermitian Hamiltonian $H$, we can generate new non-Hermitian operators sequentially, producing a virtually infinite chain of non-Hermitian Hamiltonians which are isospectral to $H$ and $H^{†}$ and whose eigenvectors we can easily deduce in an almost automatic way; no ingredients are necessary other than $H$ and its eigensystem. To set off the chain and keep it running, we use, for the first time in our knowledge, a series of maps all connected to different metric operators. We show how the procedure works in several physically relevant systems. In particular, we apply our method to various versions of the Hatano-Nelson model and to some PT-symmetric Hamiltonians.

arXiv commentin press in Annals of Physics

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Cited by in corpus (4)

• Non-Hermitian skin effect as an impurity problem
• Uncertainty Relation for Non-Hermitian Systems
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
• Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations