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(a) Trace distance of the states and as a function of time for a two-site system (dimer) in the hierarchy equation of motion model. The trace distance evolves from maximally distinguishable (=1) for the initial states to indistinguishable (=0) for the thermal equilibrium state. At intermediate times, the trace distance increases, which is due to a reversal of the information flow. Various bath correlation times are shown, 150 fs (blue), 100 fs (red), and 50 fs (yellow). For long correlation times, that is, a bath with more memory, the regions of increasing trace distance are more pronounced. (b) The distance in Eq. (4) illustrates the information content in the non-Markovian degrees of freedom of this model for the same system, initial states, and bath correlation times as in (a). The anticorrelated oscillations of the two figures show the information flow between the system and the NM degrees of freedom.
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Non-Markovianity as a function of the parameters of a dimer system (a)–(d), and the Fenna–Matthews–Olson complex (e) and (f), in the hierarchy equation of motion approach. For the dimer: (a) coupling J 12, (b) site energy difference , (c) bath dissipation rate (which is related to the bath correlation time by ,), and (d) reorganization energy (log-scale). The solid lines are calculations of Eq. (2) with the initial states being and , while the dots are calculations of NM-itymax, i.e., with optimized initial states. Dashed line segments indicate that a parameter was scanned beyond the validity of the truncation condition. For the FMO complex: (e) bath dissipation rate and (f) reorganization energy. In all figures, except in (c) and (e), we use the different bath correlation times: 50 fs (blue), 100 fs (purple), and 150 fs (red).
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Non-Markovian and nonequilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton–phonon coupling. In this work, we utilize a recently developed measure for non-Markovianity to elucidate the exciton–phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong coupling effects and nonequilibrium molecular reorganization. We propose an additional trace distance measure for the information flow that could be extended to other master equations. We find that for a model dimer system and for the Fenna–Matthews–Olson complex the non-Markovianity is significant under physiological conditions.
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