QUANTUM-MECHANICAL DISSIPATION - FROM THE WEAK-COUPLING TO THE STRONG-COUPLING LIMIT

We study a spin-1/2 entity interacting with a set of quantum-mechanical oscillators using the Heisenberg picture. In the weak-coupling limit, the Heisenberg equation is given an analytical solution, suggesting that upon increase of the coupling the system should exhibit a critical transition to an overdamped regime, like that of a heavily damped oscillator. Thus the lifetime of the trapped state increases with increasing temperature. Under the assumption of very small tunneling frequency, another analytical solution is found, which predicts the occurrence of trapped states, whose lifetime decreases with an increase of temperature. As a result of the competition between the two trapping processes, the lifetime of the localized state is shown to be a nonmonotonic function of temperature with a minimum lifetime at a certain critical value of temperature. The predictions of this theoretical treatment are carefully checked by numerical solution of the interaction between a 1/2-spin entity and a dissipative oscillator, and a very satisfactory agreement between theory and numerical solution is found over the whole range of coupling strength. © 1990 The American Physical Society.