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

1997/10/02 by Valery P. Karassiov, Karassiov, Valery P.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9710012

19 pages, LATEX

arxiv created 1997/10/02 · arxiv updated 2009/12/01

Abstract

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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