TY - JOUR
T1 - Solution of two-mode bosonic Hamiltonians and related physical systems
AU - Koç, R.
AU - Tütüncüler, H.
AU - Koca, M.
PY - 2004/10
Y1 - 2004/10
N2 - 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.
AB - 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.
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U2 - 10.1393/ncb/i2003-10097-0
DO - 10.1393/ncb/i2003-10097-0
M3 - Article
AN - SCOPUS:18444401147
VL - 119
SP - 909
EP - 920
JO - II Nuovo Cimento B Series 11
JF - II Nuovo Cimento B Series 11
SN - 0369-3554
IS - 10
ER -