Microscopic calculation of absorption spectra of macromolecules: An analytic approach

We develop a cross-disciplinary approach to analytically compute optical response functions of open macromolecular systems by exploiting the mathematical formalism of quantum field theory (QFT). Indeed, the entries of the density matrix for the electronic excitations interacting with their open dissipative environment are mapped into vacuum-to-vacuum Green’s functions in a fictitious relativistic closed quantum system. We show that by re-summing appropriate self-energy diagrams in this dual QFT, it is possible to obtain analytic expressions for the response functions in Mukamel’s theory. This yields physical insight into the structure and dynamics of vibronic resonances, since their frequency and width is related to fundamental physical constants and microscopic model parameters. For illustration, we apply this scheme to compute the linear absorption spectrum of the Fenna-Matthews-Olson light harvesting complex, comparing analytic calculations, numerical Monte Carlo simulations, and experimental data.