On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms

Abstract

The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their spectrum. The superpotential that links these systems is complex-valued, parameterized by the solutions of the Ermakov equation, and may be expressed either in nonlinear form or as the logarithmic derivative of a properly chosen complex-valued function. The non-Hermitian systems can be constructed to be either parity-time-symmetric or non-parity-time-symmetric.

arXiv comment9 pages, 2 figures (affiliation institution corrected)

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Cited by in corpus (9)

• PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry
• Exact solutions for time-dependent non-Hermitian oscillators: classical and quantum pictures
• Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM
• Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
• Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians
• Unconventional steady states and topological phases in an open two-level non-Hermitian system
• Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials
• Optical ladder operators in the Glauber-Fock oscillator array
• Non-hermitian Dirac Hamiltonian in the presence of local Fermi velocity