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Quantum Propagation of Electronic Excitations in Macromolecules: A Computationally Efficient Multi-Scale Approach

We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long time intervals. All the parameters of the underlying microscopic Hamiltonian are obtained from \emph{ab-initio} electronic structure calculations, ensuring chemical detail. In the short-time regime, the theory is solvable using a diagrammatic perturbation theory, enabling analytic insight. To compute the time evolution of the density matrix at intermediate times, typically $\lesssim$~ps, we develop a Monte Carlo algorithm free from any sign or phase problem, hence computationally efficient. Finally, the dynamics in the long-time and large-distance limit can be studied combining the microscopic calculations with renormalization group techniques to define a rigorous low-resolution effective theory. We benchmark our Monte Carlo algorithm against the results obtained in perturbation theory and using a semi-classical non-perturbative scheme. Then we apply it to compute the intra-chain charge mobility in a realistic conjugate polymer.