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

Symmetry Integrability and Geometry-Methods and Applications

article

Omar Cherbal¹  Mahrez Drir¹  Mustapha Maamache²  Dimitar A. Trifonov³ 

[1] Faculty of Physics, Theoretical Physics Laboratory;Laboratoire de Physique Quantique et Systemes Dynamiques, Department of Physics, Setif University;Institute of Nuclear Research

关键词: pseudo-Hermitian quantum mechanics;    supersymmetry;    supercoherent states;   

DOI  :  10.3842/SIGMA.2010.096

来源: National Academy of Science of Ukraine

【 摘 要 】

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 =ω J 3 +α J − +β J + , α≠β, 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.

【 授权许可】

Unknown