How Markovian is exciton dynamics in purple bacteria?

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.

Structure and Efficiency in Bacterial Photosynthetic Light Harvesting

“…A further concern is the possible role of nonmarkovianity in the system–bath coupling. , However, we find that the global Lindblad approach gives good qualitative agreement with preliminary calculations on small model systems using the exact hierarchical-equations-of-motion (HEOM) approach…”

The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials

“…A significant point about Equation 34 is that it is applicable to arbitrary form of spectral densities, which is very important since more and more studies have stressed that the realistic highly structured environment might play a crucial role in various cases like the enhancement of energy transfer rate and non‐Markovianity, the long‐sustained quantum coherence in light‐harvesting complexes, and the fine‐tuning of the dephasing and relaxation time in quantum information processors . What's more, since the concrete form of α res ( t ) which exerts a substantial influence on the numerical performance of Equation 34, has not yet been specified, this flexibility allows us to seek for a balance point between high accuracy and affordable computational cost.…”