2006/04/12 by Carla Figueira de Morisson Faria, C Figueira de Morisson Faria, Andreas Fring +1 · 2 citations
Mathematics · Physics and Astronomy · #Equivalence (formal languages) #Hamiltonian (control theory) #Hamiltonian system #Hermitian matrix #Monochromatic color #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Time evolution #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/29/018
published as J. Phys. A 39 (2006) 9269-9289 · 25 pages Latex, 1 eps figure, references added
arxiv created 2006/04/12 · openalex publication_date 2006/07/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.