Dissipation in Lagrangian Formalism

Abstract

This thesis examines dissipative forces in physical systems in both microscopic and quantum level. The system-environment interaction is modeled by assuming that the environment is composed of simple harmonic oscillators and that there is a linear interaction between these oscillators and the system. The classical case is solved by determining the retarded Green’s function, which yields the equation of motion of the system. For quantum dissipation, the Lindblad master equation is used to describe the time evolution of the reduced density matrix of the system, and the propagator is investigated to identify important parameters, including the term of Newton's friction force.