Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent S U ( 1 , 1 ) and S U ( 2 ) systems — Exact solution and geometric phase in pseudo-invariant theory

Nadjat Amaouche, Maroua Sekhri, Rahma Zerimeche +2 more

Physics OpenNov 21, 20224 citations

arXiv:0711.3887 · International Journal of Theoretical Physics

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- $\mathcal{PT}$ -symmetrySpherical-separability of Non-Hermitian Hamiltonians and Pseudo- $\mathcal{PT}$ -symmetry

Omar Mustafa, S. Habib Mazharimousavi

Published Jul 21, 2008• 3 citations

arXiv HTML PDF

DOI: 10.1007/s10773-008-9794-y

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Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent S U ( 1 , 1 ) and S U ( 2 ) systems — Exact solution and geometric phase in pseudo-invariant theory

Nadjat Amaouche, Maroua Sekhri, Rahma Zerimeche +2 more

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.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.

Physics OpenNov 21, 20224 citations

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo-

\mathcal{PT}

-symmetry

A family of spherical non-Hermitian potentials is studied. It is shown that the corresponding non-Hermitian Hamiltonians admit some "new" P

phi

phi

-symmetry. It is observed that whilst such P

phi

phi

-symmetric Hamiltonians just copy the eigenvalues of V(r), the corresponding wavefunctions would rather indulge some new probabilistic interpretations due to the change in the azimuthal part.