Quantum Transport in Macromolecules: An Effective Field Theory Approach

Transport of quantum excitations in macromolecular systems is still a very active and open field of research. In particular, several key issues have not been fully clarified yet. These include the role played by molecular thermal fluctuations and possible correlations between the degree of quantum coherence and the efficiency of the transport process. In order to gain some insight, we developed a rigorous and systematic framework describing quantum transport, based on a field-theoretic formalism.
Starting from a microscopic tight binding model coupled to the conformational dynamics of the molecule, we recover an effective field theory, for the quantum transport, in which the effect of the molecular vibrations and of dissipation is described by effective interactions.
In the short-time regime, it is possible to compute the real-time evolution of the density matrix perturbatively using Feynman diagrams technique. For illustration purposes, we study the loss of quantum coherence of holes propagating through a 3-methylthiophene polymer, identifying effective interactions responsible for de-coherence and re-coherence phenomena.
The same formalism is also extended to investigate the dynamics in the long-time limit, using the renormalization group formalism. We show that, at very low spatial resolution, this quantum transport theory reduces to a modified Brownian process.