Algebraic approach and Berry phase of a Hamiltonian with a general SU (1, 1) symmetry
- 1 July 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (7), 071701
- https://doi.org/10.1063/5.0027957
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.Funding Information
- Instituto Politécnico Nacional (SIP 20210734)
This publication has 42 references indexed in Scilit:
- Relativistic quantum mechanics with trapped ionsNew Journal of Physics, 2011
- Berry phase in arbitrary dimensionsJournal of Physics A: Mathematical and Theoretical, 2010
- Dirac Equation and Quantum Relativistic Effects in a Single Trapped IonPhysical Review Letters, 2007
- Analytic representations in quantum mechanicsJournal of Physics A: General Physics, 2006
- Generalized two-mode harmonic oscillator model: squeezed number state solutions and nonadiabatic Berry’s phaseThe European Physical Journal D, 2004
- The su(1,1) Tavis-Cummings modelJournal of Physics A: General Physics, 1998
- Exact solution of generalized Tavis - Cummings models in quantum opticsJournal of Physics A: General Physics, 1996
- Berry’s phase in the degenerate parametric amplifierPhysical Review A, 1989
- Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic OscillatorsJournal of Mathematical Physics, 1968
- Exact Solution for an-Molecule—Radiation-Field HamiltonianPhysical Review B, 1968