Effects of Dissipative Environments on Some Quantum Systems.

The properties of a system coupled to an environment can be dramatically changed compared to those of the isolated case. In this thesis I present a theoretical study of environmental influence on the following physical phenomena: the persistent current of a metallic ring, the escape rate of an electron from a helium surface, and the transition probability of the Landau-Zener level crossing. Chapter one contains a general introduction to these physical systems and a brief review of the theoretical methods I shall use. The study of an equilibrium property, the persistent current of a metallic ring coupled to an environment, is in chapter two. Chapter three describes the effects of an environment on the escape of electrons from a helium surface. In chapter four a detailed study of the Landau-Zener level crossing problem with a dissipative environment is presented. Finally, in chapter five I propose some questions that need further theoretical consideration.