Quantum Brownian motion by path integral mothod

Abstract

The purpose of this thesis is to apply the path integral method เท quantum Brownian motion theory to study the problem of a vortex in superfluid or superconductor escaping out of a metastable potential. Because of the presence of the Magnus force, after obtaining the expression for the effective action, the anomalous dam ping kernel becomes an important role in this problem. Out of the parameters contained in the anomalous dam ping kernel, the frequency of the oscillation in the harmonic pinning potential in stable direction leads us to prove the existence and non-existence of the crossover temperature, and to analyses the dissipation and Magnus force effects on the crossover temperature for general damping. These can help us understand more about the change of dominating mechanism of the escape process from thermal activation to quantum tunneling. This frequency also leads us to define the localization criterion and the effective mass of a vortex. Moreover, the escape rate formula of a vortex above the crossover temperature is splatted into two different cases corresponding with difference values of this frequency.