International Journal of Modern Physics B

We review the dynamical statistical theory of the interaction of an atom with a cavity radiation field in the framework of exactly solvable Jaynes-Cummings type models.

We discuss different methods of characterizing the loss of memory of initial conditions in chaotic dynamical systems.

Third order nonlinear susceptibility of two-level atoms dressed by the cavity vacuum is studied to see the effect of Rabi oscillations. It is found that while the interference effects remove the peaks of on-resonance third harmonic generation, peak splitting is seen for Raman scattering and two photon processes.

We carry out a revision of the mechanism of anyon superconductivity found in the Random Phase Approximation. It is shown that the Debye screening of a statistical Coulomb-like interaction produced by contributions beyond the RPA destroys the abovementioned mechanism. The linear mode appeared in the particle-hole channel within the RPA is identified with a finite damping zero-sound. As an alternative mechanism an attraction of anyons which could lead to a formation of boson composites is observed. A finite temperature phase transition, hydrodynamics and electrodynamics of anyon system are described from this alternative point of view.

The two-dimensional six-vertex model with a particular choice of external field is known to be equivalent to a theory of free Fermions. Two conditions are made on the six-vertex weights. A simple physical interpretation of the ordered and disordered phases is found. The Fermi sea is filled and the free energy, correlation length, order parameter, correlation functions and phase diagram are determined.

A three-dimensional statistical system, called here the six-edge model, is shown, for a particular domain of parameters, to be equivalent to a theory of Fermionic strings. This model has a local U(1) gauge invariance, similiar to the global invariance of the two-dimensional six-vertex model. Further restricting the parameters gives a system named here the five-edge model, which is exactly solvable. The conformal anomaly of the surfaces is calculated. The transfer matrix is diagonalized, and the free energy, phase diagram and correlation length are determined exactly. The surfaces of the model display a roughening transition similiar to that analyzed by Blöte, Hilhorst and Nienhuis.