Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics

Abstract

We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.

Generalized spin mapping for quantum-classical dynamics

“…In the future we expect that the accuracy can be extended to longer times by combining the dynamics with a general-ized quantum master equation, as has been successfully done for other mapping approaches. [78][79][80][81] Another natural extension would be to develop an FBTS or PLDM method based on spin mapping. Finally, we also believe that the spin mapping will be relevant in the search for a nonadiabatic extension to ring-polymer molecular dynamics.…”

On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics

“…40 The benefits of this include a noticeable gain in accuracy as well as the ability to obtain long time dynamics using only short time trajectories. [41][42][43][44] A similar motivation underlies the approach presented here, albeit using a simpler strategy. First we recast the observable of interest in terms of a correlation function involving the identity operator.…”

Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics

“…In contrast, MF-GQME produces highly accurate results, consistent with previous observations that this scheme offers significant improvements over direct MFT in nonadiabatic regimes. [21][22][23] For this nonadiabatic problem, the memory kernel decays by a cutoff time of τ c = 0.15 ps, which is considerably shorter than the 1-2 ps lifetime of the population dynamics. However, because MF-GQME requires sampling 28 distinct initial conditions to generate the memory kernel, uniform sampling of all initial conditions in this regime, i.e., when trajectories are apportioned equally to each initial condition, requires a total of 10 5 total trajectories (∼3,500 per initial condition) to converge the memory kernel.…”

“…23 For all LHCII dynamics shown, we used τ c = 65 fs. The instabilities observed for LHCII might be able to be alleviated by employing alternative closures, 23,43,44 or by using higher level quantum-classical methods to generate the memory kernel. 20,24 After calculating the partial memory kernels, the GQME, Eq.…”

“…Here, we choose the N s state system generalization of the Redfield-type projection operator, shown in Ref. 23 in the context of a two-level system. In the more conventional Nakajima-Zwanzig form of the GQME for nonequilibrium RDM dynamics, 1,2 this projector corresponds to the commonly used Argyres-Kelley projector, 63 P, which performs a partial trace over the bath and multiples by the canonical density of the bath, i.e., P(Ô bÔs ) =ρ eq b Tr b [Ô bÔs ] = ρ eq bÔ s Tr b [Ô b ], whereÔ b andÔ s are bath and system operators, respectively.…”