Exactly solvable time-dependent non-Hermitian quantum systems from point transformations

Fring, A. ORCID: 0000-0002-7896-7161 & Tenney, R. (2021). Exactly solvable time-dependent non-Hermitian quantum systems from point transformations. Physics Letters A, 410, 127548. doi: 10.1016/j.physleta.2021.127548

Abstract

We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. Initially we identify a point transformation as a map from an exactly solvable time-independent system to an explicitly time-dependent non-Hermitian Hamiltonian system. Subsequently we employ the point transformation to construct the non-Hermitian time-dependent invariant for the latter system. Exploiting the fact that this invariant is pseudo-Hermitian, we construct a corresponding Dyson map as the adjoint action from a non-Hermitian to a Hermitian invariant, thus obtaining solutions to the time-dependent Dyson and time-dependent quasi-Hermiticity equation together with solutions to the corresponding time-dependent Schrödinger equation.

Publication Type:	Article
Additional Information:	© 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Non-Hermitian quantum systems, Point transformations, PT-symmetric systems, Lewis-Riesenfeld invariants, Swanson model
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics