Semiclassical Dynamics of SU (2) Models

Miguel Baltazar, Ivan F. Valtierra, A. B. Klimov

We derive the explicit differential form for the action of the generators of the SU(1,1) group on the corresponding s-parametrized symbols. This allows us to obtain evolution equations for the phase-space functions on the upper sheet of the two-sheet hyperboloid and analyze their semiclassical limits. Dynamics of quantum systems with SU(1,1) symmetry governed by compact and non-compact Hamiltonians are discussed in both quantum and semiclassical regimes.

Shainen M. Davidson, Dries Sels, Anatoli Polkovnikov

Claudia M. Sarris, Araceli N. Proto

P. K. Aravind

The semiclassical Dicke model and the ideal parametric amplifier are described by Hamiltonians linear in the SU(2) and SU( 1,1) group generators, respectively. We use the usual pseudospin vector as well as its SU(1,1) analog1 to give a unified description of the dynamics of the coherent states in these models. The pseudospin dynamics is governed by a precession (or pseudoprecession) equation, hence simple geometrical arguments can be used to infer the evolution of the coherent state parameters. To study fluctuations and squeezing we introduce a correlation tensor which is a higher-order generalization of the pseudospin vector. The correlation tensor obeys a generalized precession equation which can be factored into scalar, vector, and quadrupole parts and solved exactly by application of the Cayley-Hamilton theorem. Our approach to the calculation of squeezing and fluctuations provides an alternative to the more traditional approach employing disentangling theorems. It also provides an attractive and closely parallel geometrical description of coherent state evolution and squeezing in the two models.

Claudia M. Sarris, R. O. Hansen, Angelo Plastino

Andrei B Klimov, Hossein T. Dinani, Zachari E D Medendorp +1 more

We introduce a concept of squeezing in collective qutrit systems through a geometrical picture connected to the deformation of the isotropic fluctuations of su (3) operators when evaluated in a coherent state. This kind of squeezing can be generated by Hamiltonians nonlinear in the generators of su (3) algebra. A simplest model of such a nonlinear evolution is analyzed in terms of semiclassical evolution of the SU (3) Wigner function.