Open Quantum Dynamics On Lie Group: An Effective Field Theory Approach

Abstract

In this thesis, we address construction of effective action for the dissipative systems whose configuration space coincides with a Lie group. We start by generalizing the classical system plus reservoir model to the case of position dependent Ohmic dissipation. This is achieved by coupling the system to a field living in one extra dimension. Then, employing the Schwinger-Keldysh technique, we construct the general influence functional for a system on a Lie group which includes the classical contribution and the first quantum correction within the linear response approximation. Abandoning the linear response assumption, we generalize the results by requiring the invariance under the dynamical Kubo-Martin-Schwinger symmetry. This gives us the most general influence functional with nonlinearly realized symmetry. We explore its systematic reduction to the case of strictly Ohmic dissipation. Finally, we revisit the field theoretic model of the bath and show that it produces both the leading and first subleading parts of the most general influence functional at high temperature.