Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory
Nadjat Amaouche,
Maroua Sekhri,
Rahma Zerimeche,
Mustapha Maamache,
J.-Q. Liang
Affiliations
Nadjat Amaouche
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, Algeria
Maroua Sekhri
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, Algeria
Rahma Zerimeche
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, Algeria; Physics Department, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel, Algeria
Mustapha Maamache
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, Algeria; Corresponding author.
J.-Q. Liang
Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, Shanxi 030006, China
In this paper we investigate time-dependent non-Hermitian Hamiltonians, which consist of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1) and SU(2) systems in a unified manner. Then, we derive the Lewis–Riesenfeld (LR) phase, which can be separated into the dynamic and the geometrical phases. The analytical results are well consistent with those of the corresponding Hermitian Hamiltonians reported in the literature.
