Sl(2) variational schemes for solving one class of nonlinear quantum models

Abstract

Hamiltonians of a wide-spread class of G inv invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as nonlinear functions of sl(2) generators. This enables us to use variational schemes, based on sl(2) generalized coherent states as trial functions, to obtain new ( sl(2) cluster) quasi-classical solutions of spectral and evolution tasks which smoothly approximate exact ones and catch explicitly quantum cooperative features of the models under study (in contrast with standard independent-mode quasi-classical approximations). In such a way new analytical expressions are found for the energy spectra which are beyond both equidistant and quasi-equidistant ones obtained earlier.