International audienceWe compare four different types of equations of motion for reduced density matrix of a system of molecular excitons interacting with thermodynamic bath. All four equations are of second order in the linear system-bath interaction Hamiltonian, with different approximations applied in their derivation. In particular we compare time-nonlocal equations obtained from so-called Nakajima-Zwanzig identity and the time-local equations resulting from the partial ordering prescription of the cummulant expansion. In each of these equations we alternatively apply secular approximation to decouple population and coherence dynamics from each other. We focus on the dynamics of intraband electronic coherences of the excitonic system which can be traced by coherent two-dimensional spectroscopy. We discuss the applicability of the four relaxation theories to simulations of population and coherence dynamics, and identify features of the two-dimensional coherent spectrum that allow us to distinguish time-nonlocal effects
A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte-Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.
We demonstrate the application of the recently introduced parametric projector operator technique to a calculation of the second order non-linear optical response of a multilevel molecular system. We derive a parametric quantum master equation (QME) for the time evolution of the excited state of an excitonic system after excitation by the first two pulses in the usual spectroscopic four-wave-mixing scheme. This master equation differs from the usual QME by a correction term which depends on the delay τ between the pulses. In the presence of environmental degrees of freedom with finite bath correlation time and in the presence of intramolecular vibrations we find distinct dynamics of both the excite state populations and the electronic coherence for different delays τ .
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