The Semiclassical Theory of the t — J Model

Steven M. Rinaldi

Abstract : A semiclassical analysis of injected lasers with stable and unstable resonators and arbitrary outcoupling fractions was performed. Homogeneously broadened lasers with Fabry-Perot and with positive branch, confocal unstable resonators were modeled. Both time-dependent and steady-state analyses of free-running and injected lasers were performed. Because of deficiencies in the standing wave semiclassical and the simple saturable gain models, a new semiclassical theory of homogeneously broadened lasers were developed. The theory is predicted upon the following assumptions: the atoms are two-level, a single longitudinal mode exists in the cavity, the transverse mode structure can be adequately modeled by the geometric optics mode, and the laser electric fields can be described by a pair of counterpropagating planar, cylindrical, or spherical traveling waves with different amplitudes. A general semiclassical theory was first developed, and then specialized to the Fabry-Perot and positive branch, confocal unstable resonator cases. Both the Maxwell-Bloch and rate equation approximation forms of the theory were derived. The general theory is sufficiently broad to allow the modeling of the geometric optics mode of any standing wave resonator configuration. The theory was shown to reduce to the simple saturable gain and standing wave semiclassical models in the appropriate limits. The analysis of the injected lasers were performed with the new semiclassical theory. Both time-dependent and steady-state analyses were performed.

Christian Grosche, Frank Steiner

A. Matzkin

The "dynamical mismatch" observed in quantum systems in the semiclassical regime challenge the Pilot wave model. Indeed the dynamics and properties of such systems depend on the trajectories of the classically equivalent system, whereas the de Broglie-Bohm trajectories are generically non-classical.\ In this work we examine the situation for the model favoured by de Broglie, the theory of the Double Solution (DS). We will see that the original DS model applied to semiclassical systems is also prone to the dynamical mismatch.\ However we will argue that the DS theory can be modified in order to yield propagation of the singularity in accord with the underlying classical dynamics of semiclassical systems.

Cécile DeWitt-Morette

Andrea Sacchetti

Ángela M. Guzmán, Pierre Meystre, Ewan M. Wright

We present a semiclassical theory of the micromaser by using a consistent multiple-time-scale expansion of its dynamics. The time scale over which the semiclassical approximation is valid is established, and the effects of quantum and thermal fluctuations in the long-time limit are investigated. A thermodynamical analogy is introduced to interpret the steady-state properties of the micromaser, and we show that a simple model allowing for two-phase coexistence provides the best agreement between the semiclassical and quantum theories.