Abstract
This thesis presents an extension to the Caldeira-Leggett system-plus-bath model through
the introduction of a damped environment using Caldirola-Kanai Lagrangians. By using
a path integral approach for a deterministically driven and damped harmonic oscillator
we construct an influence functional and consequently derive a master equation for the reduced density matrix of a system in a damped environment. This model is compared to
its classical analogue and a system which is exponentially decoupled from its environment.
Small changes are observed in the decoherence times of the damped model compared with
the undamped one, which is found to be caused by a new potential term in the damped
master equation. In weakly damped baths, we see that this term causes a particles position probability distribution to diffuse more quickly and a reduction in transfer rates over
or through a barrier in a double well potential. We expand upon this work through the
introduction of a phenomenologically noisy bath using a stochastic Schr¨odinger equation
approach, thus constructing a quantum model of hierarchical, stochastic environments. Finally, we discuss how our models may be taken further and what consequences that may
have in understanding the emerging field of quantum biology.