Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry

Abstract

In this paper we study a general Hamiltonian with a linear structure given in terms of two different realizations of the $SU(1,1)$ group. We diagonalize this Hamiltonian by using the similarity transformations of the $SU(1,1)$ and $SU(2)$ displacement operators performed to the $su(1,1)$ Lie algebra generators. Then, we compute the Berry phase of a general time-dependent Hamiltonian with this general $SU(1,1)$ linear structure.

arXiv comment11 pages

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Cited by in corpus (3)

• $SU(1,1)\times SU(2)$ approach and the Mandel parameter to the Hamiltonian of two oscillators with weak coupling
• Algebraic analysis of non-Hermitian quadratic Hamiltonians
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties