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

• Main Authors: Cherbal, O., Drir, M., Maamache, M., Trifonov, D.A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/146526

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=ωJ₃+αJ₋+βJ₊, 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.