ディコヒーレンスと緩和現象の物理　　Coleman-Hepp 模型とその周辺　　

Decoherence phenomena of quantum systems have long been studied in connection with measurement processes in quantum mechanics and also with relaxation processes in various fields. The latter is intimately related with non-equilibrium statistical mechanics and there are several milestones. Most of these theories are formulated within lower order perturbational method. That is, interactions between a relevant system and its surrounding (reservoir) are assumed to be weak enough. There are, however, several cases where strong interactions play an essential role. Typical examples are low field resonance and muon spin rotation(relaxation). In treating these problems, we cannot use the lower order perturbation theories, and therefore, we have to solve completely dynamical evolution of the quantum systems. To our knowledge, there have been only a few theoretical models which can be solved rigorously giving physically non-trivial results. One of such exactly solvable models is a special case of a stochastic model of low field resonance and relaxation. The rigorous solution is obtained by two different methods. In this seminar, we study another exactly solvable model of decoherence. This is the so-called Coleman-Hepp model, which was originally introduced in order to gain certain insights into the quantum mechanical measurement process, and there have been several generalized theories of the model. We use a slightly modified version of a generalized Coleman-Hepp model to give a rigorous solution on the basis of the spin coherent state representation. Thus we can discuss dynamical behavior of the detector system as well as that of an incident particle. Time evolution of averaged physical quantities and quasi-probability density are explicitly given.