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Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories

Fring, A. ORCID: 0000-0002-7896-7161, Taira, T. & Tenney, R. (2022). Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories. Physics Letters A, 452, 128458. doi: 10.1016/j.physleta.2022.128458

Abstract

C-operators were introduced as involution operators in non-Hermitian theories that commute with the time-independent Hamiltonians and the parity/time-reversal operator. Here we propose a definition for time-dependent -operators and demonstrate that for a particular signature they may be expanded in terms of time-dependent biorthonormal left and right eigenvectors of Lewis-Riesenfeld invariants. The vanishing commutation relation between the -operator and the Hamiltonian in the time-independent case is replaced by the Lewis-Riesenfeld equation in the time-dependent scenario. Thus, -operators are always Lewis-Riesenfeld invariants, whereas the inverse is only true in certain circumstances. We demonstrate the working of the generalities for a non-Hermitian two-level matrix Hamiltonian. We show that solutions for and the time-dependent metric operator may be found that hold in all three -regimes, i.e., the -regime, the spontaneously broken -regime and at the exceptional point.

Publication Type: Article
Additional Information: © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Publisher Keywords: -symmetry, Lewis-Riesenfeld invariants, C-operators, Non-Hermitian systems, Time-dependent systems
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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