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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2010, том 6, 096, 11 стр. (Mi sigma554)

Эта публикация цитируется в 9 статьях

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

Omar Cherbala, Mahrez Drira, Mustapha Maamacheb, Dimitar A. Trifonovc

a 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

Аннотация: 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.

Ключевые слова: pseudo-Hermitian quantum mechanics; supersymmetry; supercoherent states.

MSC: 81Q12; 81Q60; 81R30

Поступила: 29 сентября 2010 г.; в окончательном варианте 4 декабря 2010 г.; опубликована 15 декабря 2010 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2010.096



Реферативные базы данных:
ArXiv: 1009.5293


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