Some problems on macroscopic quantum phenomena and Josephson junctions

This thesis contains basically two parts. In the first part, the theory of quantum dynamics of a general particle in fermionic heat baths is considered. In contrast to the existing work in the literature, we employ a path-integral formalism with fermions being treated in Grassmann algebra. Working on this formalism, we are able to investigate many interesting systems. Our main goal is on the mapping between fermion baths and boson baths. Two major methods are used respectively, and the mapping has been achieved in several practically important cases. The second part is concerned with the experimental test of macroscopic quantum phenomena in systems of Josephson junction(s). In trying to determine in general the parameters of Josephson junction (this determination is essential for the test), we investigate the bottom part of the "return" I-V characteristic of a current-biased junction. We show that this investigation can indeed lead to a quantitative determination of the parameters. Moreover, we also study an important phenomenon associated with the problem, the quantum (as well as classical) fluctuation-induced retrapping, and interesting predictions have been made.