Solution of two-mode bosonic Hamiltonians and related physical systems
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We have constructed the quasi-exactly-solvable two-mode bosonic realizations of su(2) and su(1, 1) algebra. We derive the relations leading to the conditions for quasi-exact solvability of two-boson Hamiltonians by determining a general procedure which maps the Schwinger representations of the su(2) and su(1, 1) algebras to the Gelfand-Dyson representations, respectively. This mapping allows us to study nonlinear quantum-optical systems in the framework of quasi-exact solvability. Our approach also leads to a simple construction of special functions of two variables which are the most appropriate functions to study quasi-probabilities in quantum optics.
Keywords
Cite
@article{arxiv.math-ph/0504072,
title = {Solution of two-mode bosonic Hamiltonians and related physical systems},
author = {Ramazan Koc and Hayriye Tutunculer and Mehmet Koca},
journal= {arXiv preprint arXiv:math-ph/0504072},
year = {2007}
}