Abstract
We investigate the extent to which the dynamics of excitons in the light-harvesting complex LH2 of purple bacteria can be described using a Markovian approximation. To analyse the degree of non-Markovianity in these systems, we introduce a measure based on fitting Lindblad dynamics, as well as employing a recently introduced trace-distance measure. We apply these measures to a chromophore-dimer model of exciton dynamics and use the hierarchical equation-of-motion method to take into account the broad, low-frequency phonon bath. With a smooth phonon bath, small amounts of non-Markovianity are present according to the trace-distance measure, but the dynamics is poorly described by a Lindblad master equation unless the excitonic dimer coupling strength is modified. Inclusion of underdamped, high-frequency modes leads to significant deviations from Markovian evolution in both measures. In particular, we find that modes that are nearly resonant with gaps in the excitonic spectrum produce dynamics that deviate most strongly from the Lindblad approximation, despite the trace distance measuring larger amounts of non-Markovianity for higher frequency modes. Overall we find that the detailed structure in the high-frequency region of the spectral density has a significant impact on the nature of the dynamics of excitons.
Highlights
Photosynthesis provides the energy for most life on Earth
Using the hierarchical equations-of-motion (HEOM) approach60 as implemented in the Phi software package,64 we modelled the effect of the Brownian spectral density on a symmetric dimer parameterised to reflect a dimer of the LH2 complex of purple bacteria
Taking into account the differences between the exact calculation and the Lindblad seen here and our results earlier in Figure 6, where we showed that non-Markovianity increases as a more detailed structure is included in the spectral density, and considering our density functional theory (DFT) calculations which show that there are many more intra-molecular modes that have been excluded from this particular calculation, the evidence suggests that a Lindblad equation would no longer be able to reproduce the dynamics for a realistic spectral density
Summary
Photosynthesis provides the energy for most life on Earth. The conversion of light energy into biologically useful chemical energy is a complex process performed by a variety of different organisms. Other measures are based upon the sign of decay rates of a Lindblad master equation in its canonical form and properties of the affine transform induced by the dynamical map.. Other measures are based upon the sign of decay rates of a Lindblad master equation in its canonical form and properties of the affine transform induced by the dynamical map.52 Some of these measures are complete in the sense that they capture any deviation away from the Markovian regime, whilst others capture only particular aspects of non-Markovianity. The complete measures either require information on the dynamical map or the use of an ancillary system which incurs extra, often impractical, computational cost To tackle this issue we have developed a measure of non-Markovianity based upon finding the closest fitting Lindblad master equation. In practice we used 105 pure initial states selected to uniformly cover the surface of the Bloch sphere
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