Non-Hermitian Hamiltonians and similarity transformations

Abstract

We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like transformation and its generalization. Such similarity transformations also reveal the connection with pseudo-Hermiticity in a simple and straightforward way. In addition to it we consider the positive and negative eigenvalues of a three-parameter non-Hermitian oscillator.

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Cited by in corpus (5)

• Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Hofstadter-Toda spectral duality and quantum groups
• Understanding Partial PT symmetry as weighted composition conjugation in Reproducing Kernel Hilbert Space :An application to non-hermitian Bose-Hubbard type Hamiltonian in Fock space
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity