Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States

Omar Cherbal ; Mahrez Drir ; Mustapha Maamache ; Dimitar A. Trifonov

Symmetry, integrability and geometry: methods and applications, Tome 6 (2010)

Résumé

A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $H=\omega J_3+\alpha J_{-}+\beta J_+$, $\alpha\neq\beta$, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.

Détail

Keywords: pseudo-Hermitian quantum mechanics; supersymmetry; supercoherent states.

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