Population of site 1 as a function of time (in ps) for a two state model (Ref. 32). Exciton state energy gap is , excitonic coupling is , temperature is , characteristic time of the phonon bath is , and solvent reorganization energy is varied from [panel (a)], [panel (b)], [panel (c)], and [panel (d)]. Both the ILDM and Landmap results are calculated using the nonadiabatic dynamics theory outlined in this paper. Results labeled Tao–Miller were computed using the linearized semiclassical initial value representation theory and are taken from Ref. 38. Results labeled Ishizaki–Fleming were generated using the hierarchical coupled reduced master equation approach and are taken from Ref. 32 as were the results generated using Redfield theory.
Same as Fig. 1 except now the characteristic relaxation time for the phonon bath is .
Comparison of results from NMQJ and ILDM propagation calculations of populations and coherences for the second simplified two state model with , , and . The bath spectral density has the Ohmic with exponential cutoff form with , and . , 77 K, and 300 K in panels (a), (b), and (c), respectively. In each panel, upper sets of curves (symmetric about 0.5) are populations, while progressively lower sets of curves are real and imaginary parts of coherence, respectively. Smoother curves in each case are NMQJ results and curves with more statistical noise are ILDM results. In these panels, x-axes give times in picoseconds. Panel (d) compares state populations computed with the NMQJ and the ILDM propagation approaches for the seven state FMO model (Refs. 14 and 33) with independent identical baths of exponentially truncated Ohmic form having and . The temperature for these FMO calculations is .
Panels (a), (b), and (c) show populations as functions of time for the seven state model (Ref. 14) with , and site 1 is initially occupied. For clarity, only states 1, 2, and 3 are plotted, although four states are included in the ILDM propagation and all seven states are included with the other propagation schemes. ILDM benchmark results are plotted for comparison in each panel. Panel (d) compares ILDM results for various concurrences with similar results obtained from the hierarchical reduced quantum master equation approach.
Panels (a) and (b) show populations as functions of time for the seven state model (Ref. 14) with and all propagations include dynamics of the full seven state Hamiltonian, although only the largest amplitude states are displayed for clarity. In panel (a), site 1 is initially occupied, while panel (b) presents results obtained with state 6 initially occupied. Panel (d) displays concurrence results obtained for the runs with and state 6 initially occupied. In these three panels ILDM and hierarchical reduced quantum master equation results are compared. Panel (c) presents results exploring convergence of the ILDM calculations with ensemble sizes trajectories, and . Results are obtained with , and state 1 initially occupied.
Results explore the effect of coupling the model FMO excitonic quantum subsystem (Ref. 14) to its environment. Panel (b) presents populations as functions of time: red, green, and blue (oscillatory) curves give site populations starting with state 1 initially occupied in the absence of bath coupling. The other curves that show damped oscillations and long time linear growth (state 3) or decay (states 1 and 2) are computed with the full bath coupling included (ILDM and hierarchical reduced master equation results are presented). Panel (a) shows effect of removing the environment coupling on quantum subsystem coherences.
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