ABSTRACT
Quantum Brownian motion is a frontier area of research in quantum optics (Louisell 1973; Sargent, Scully, and Lamb 1974; Meystre and Sargent 1991), condensed matter (Grabert, Schramm, and Ingold 1988; Weiss 1999), and chemical physics (Hänggi, Talkner, and Borkovec 1990; Zwanzig 1973) over the last several decades. The fundamental paradigm is the irregular movement of a particle in a thermal bath kept at finite temperature. The bath constitutes many, in principle, infinite degrees of freedom interacting with the particle. In general, the bath is considered to be a set of harmonic oscillators of varied frequency ranges and is therefore bosonic in character. The particle follows the reduced stochastic dynamics obtained after appropriate elimination of these reservoir degrees of freedom under suitable approximation schemes. The dynamical evolution is characterized by quantum dissipation and bosonic noise related to each other by fluctuation-dissipation (FD) relation, ensuring a detailed balance in the system. This chapter concerns a system-reservoir model where the reservoir is constituted by a set of two-level atoms or spin-1/2 systems.
