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.

11 pages

References in corpus (3)

• Progressive field-state collapse and quantum non-demolition photon counting
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Berry Phase in a Two-atom Jaynes-Cummings Model with Kerr Medium

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