Evolution operator for time-dependent non-Hermitian Hamiltonians
Abstract
The evolution operator U(t) for a time-independent parity-time-symmetric systems is well studied in the literature. However, for the non-Hermitian time-dependent systems, a closed form expression for the evolution operator is not available. In this paper, we make use of a procedure, originally developed by A.R.P. Rau [Phys.Rev.Lett, 81, 4785-4789 (1998)], in the context of deriving the solution of Liuville-Bloch equations in the product form of exponential operators when time-dependent external fields are present, for the evaluation of U(t) in the interaction picture wherein the corresponding Hamiltonian is time-dependent and in general non-Hermitian. This amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition.
Cite
@article{arxiv.1809.09377,
title = {Evolution operator for time-dependent non-Hermitian Hamiltonians},
author = {Bijan Bagchi},
journal= {arXiv preprint arXiv:1809.09377},
year = {2018}
}
Comments
10 pages; Accepted in Letters in High Energy Physics, some typos corrected and few references added