A Nonlinear $sl(2)$ Dynamics and New Quasiclassical Solutions for a Class of Quantum Coupled Systems

Details A Nonlinear $sl(2)$ Dynamics and New Quasiclassical Solutions for a Class of Quantum Coupled Systems A Nonlinear $sl(2)$ Dynamics and New Quasiclassical Solutions for a Class of Quantum Coupled Systems

1997-10-02

arxiv.org/abs/quant-ph/9710012v1

Physics

Quantum Physics

19 pages, LATEX

Scientific paper

Hamiltonians of a wide-spread class of strongly coupled quantum system models are expressed as nonlinear functions of $sl(2)$ generators. It enables us to use the $sl(2)$ formalism, in particular, $sl(2)$ generalized coherent states (GCS) for solving both spectral and evolution tasks. In such a manner, using standard variational schemes with $sl(2)$ GCS as trial functions we find new analytical expressions for energy spectra and non-linear evolution equations for cluster dynamics variables in mean-field approximations which are beyond quasi-harmonic ones obtained earlier. General results are illustrated on certain concrete models of quantum optics and laser physics.

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