Time evolution of non-Hermitian Hamiltonian systems

Details Time evolution of non-Hermitian Hamiltonian systems Time evolution of non-Hermitian Hamiltonian systems

2006-04-04

arxiv.org/abs/quant-ph/0604014v2

J. Phys. A 39 (2006) 9269-9289

Physics

Quantum Physics

25 pages Latex, 1 eps figure, references added

Scientific paper

10.1088/0305-4470/39/29/018

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.

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