Time evolution of non-Hermitian Hamiltonian systems

de Morrison Faria, C. F. & Fring, A. (2006). Time evolution of non-Hermitian Hamiltonian systems. Journal of Physics A: Mathematical and General, 39(29), pp. 9269-9289. doi: 10.1088/0305-4470/39/29/018

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Abstract

We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in addition in some cases also invariant under PT-symmetry. In particular, for the harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate explicitly various transition amplitudes, for the situation when these systems are exposed to a monochromatic linearly polarized electric field.

Item Type: Article
Uncontrolled Keywords: SYMMETRIC QUANTUM-MECHANICS, PSEUDO-HERMITICITY, PT-SYMMETRY, FIELD-THEORIES, REAL SPECTRA, STABILIZATION, OPERATOR, IONIZATION, EQUATIONS, SOLITONS
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/782

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