Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories

Abstract

We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely on prior knowledge of transition states or reactive pathways, and thus can provide mechanistic insight into ultrafast relaxation processes in addition to their associated rates. In particular, we formulate a quantum path ensemble using the stochastic realizations of an unravelled quantum master equation, which results in trajectories that can be conditioned on starting and ending in particular quantum states. Because the dynamics rigorously obeys detailed balance, rate constants can be evaluated from reversible work calculations in this conditioned ensemble, allowing for branching ratios and yields to be computed in an unbiased manner. We illustrate the utility of this method with three examples: energy transfer in a donor-bridge-acceptor model, and models of photo-induced proton-coupled electron transfer and thermally activated electron transfer. These examples demonstrate the efficacy of path ensemble methods and pave the way for their use in studying of complex reactive quantum dynamics.

Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

“…It can also be extended to lattice models, where the rate matrix has to be expressed in a variational ansatz. A system modeled by a different stochastic equation of motion, like that employing an Andersen thermostat 14 or quantum trajectory-based approaches, 83,84 can also be treated through this algorithm by changing only the functional forms of the path-actions provided a Doob transformation exists.…”

Transition Path Sampling as Markov Chain Monte Carlo of Trajectories: Recent Algorithms, Software, Applications, and Future Outlook

“…Furthermore, TPS has been applied to small quantum systems, [76,169] and non-adiabatic surface hopping. [170] Some methods to approximate quantum effects on nuclear motion involve ensembles of trajectories, and path sampling algorithms can be used to study them.…”

“…Recently, Limmer and coworkers applied TPS to a quantum master equation [ 76 ] to study rare nonadiabatic dynamics in open quantum systems.…”

Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states

“…For LDT to be applied to practical problems requires the development of robust numerical tools to compute LDFs. Monte Carlo sampling methods, such as the cloning algorithm and transition path sampling [4][5][6] augmented with importance sampling [7][8][9] as well as recent direct rate function evaluation techniques [10] have been applied to lattice and continuum nonequilibrium systems [4,6,[11][12][13][14][15][16][17][18][19][20][21][22]. Alternatively, tensor network (TN) methods provide analytic or numerical representations of the steady state of a master equation, with some common examples being the matrix ansatz [23,24] and the density matrix renormalization group (DMRG) algorithm [15,16,[25][26][27].…”