Semi-classical Models

Isaac Layton

Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental decoherence can lead to improved semi-classical theories that are exact descriptions of the original quantum dynamics. In doing so, we show how consistent models of classical-quantum dynamics can arise as effective descriptions of open quantum systems.

Joshua J. Heiner, David R. Thayer

A nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a classically driven nonlinear differential equation with dissipation and a semi-classical interpretation of the torque on a spin magnetic moment in the presence of a realistic magnetic field, which will represent two equilibrium positions. The highly complicated driven nonlinear dissipative semi-classical model is used to introduce chaos, which is necessary to produce the correct statistical quantum results. The resemblance between this semi-classical spin model and the thoroughly studied classical driven-damped nonlinear pendulum are shown and discussed.