This article is cited in 9 papers

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

Omar Cherbal^a, Mahrez Drir^a, Mustapha Maamache^b, Dimitar A. Trifonov<sup>c

a</sup> Faculty of Physics, Theoretical Physics Laboratory, USTHB, B. P. 32, El Alia, Algiers 16111, Algeria
^b Laboratoire de Physique Quantique et Systemes Dynamiques, Department of Physics, Setif University, Setif 19000, Algeria
^c Institute of Nuclear Research, 72 Tzarigradsko chaussée, 1784 Sofia, Bulgaria

Abstract: 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.

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

MSC: 81Q12; 81Q60; 81R30

Received: September 29, 2010; in final form December 4, 2010; Published online December 15, 2010

Language: English

DOI: 10.3842/SIGMA.2010.096

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ArXiv: 1009.5293