Role of fluctuations and defects in select condensed matter problems

Abstract

Defects and fluctuations dominate both static and dynamical properties of systems in the condensed phase. In this work, we focus on three such examples. Firstly, we model the effect of proton fluctuations on the rate of electron transfer in the condensed phase through an electron donor-acceptor assembly linked via an H-bonding bridge. The model suggests that it is possible for the electron transfer rate through a deuterated H-bonding assembly to exceed the rate through a protonated H-bonding bridge at low temperature, consistent with experimental findings. Next, we consider the convergence properties of Jarzynski's non-equilibrium work relation. This relation expresses the free energy change of a system, onto which finite-time work is done, as an ensemble average over all possible trajectories of the system. We quantify the regime of applicability of this equality by considering the role of rare fluctuations which dominate the work average of entropy generating processes. Lastly, we consider fluorophore lifetime variations arising when single molecules are placed near non-planar metallic surfaces. We compute the exact first order self-fields of vertical dipoles located above locally curved perfectly conducting surfaces by invoking a small slope phase perturbation technique. The results suggest that smooth perturbations lead to deviations from the image theory results extensively used to interpret the experimentally observed single molecule lifetime changes.