City Research Online

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
SWORD Depositor:	Symplectic Administrator

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