DYNAMICS OF DISSIPATIVE 2-LEVEL SYSTEMS IN THE STOCHASTIC-APPROXIMATION

The dynamics of the spin-boson Hamiltonian is considered in the stocha stic approximation. The Hamiltonian describes a two-level system coupl ed to an environment, and is widely used in physics, chemistry, and th e theory of quantum measurement. We demonstrate that the method of sto chastic approximation, a general method for consideration of dynamics of an arbitrary system interacting with environment, is powerful enoug h to reproduce qualitatively the striking results by Leggett et nl. [R ev. Mod. Phys. 59, 1 (1987)] found earlier for this model system. The results include an exact expression of the dynamics in terms of the sp ectral density, and show the appearance of two interesting regimes for the system, i.e., pure oscillating and pure damping ones. Correlators describing the environment are also computed.