English

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}
}