Figure 1

Comparisons between the dynamics given by threes models.

Time evolution of the populations ρ₊₊(t) (solid) and coherence |ρ₋₊(t)| (dashed) predicted by (a) TC2, (b) HEOM and (c) TL2 for the spin-boson model with different values of λ at temperatures T = 300 K (black), 250 K (red) and 200 K (blue). The other parameters are ω₀ = 70 cm⁻¹, J = 100 cm⁻¹ and γ = 50 cm⁻¹ (γ⁻¹ = 106 fs). For small λ, both QMEs yield excellent results, as expected. The inset in (a) shows the results given by TC2 (solid curve) and HEOM(dot-dashed curve) for λ = 5 cm⁻¹ and T = 250 K, illustrating how they almost overlap. However, due to over-estimation of the coherence, the result calculated from the TC2 method shows a slightly higher beating behavior in the population dynamics. In contrast, for large λ the population dynamics predicted by the TC2 method is in better agreement with those of the HEOM, whereas the populations given by the TL2 method are somewhat sluggish and tend to approach thermal equilibrium a bit faster.