Improving long time behavior of Poisson bracket mapping equation: a non-Hamiltonian approach.
Understanding nonadiabatic dynamics in complex systems is a challenging subject. A series of semiclassical approaches have been proposed to tackle the problem in various settings. The Poisson bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner. Operationally, it is expressed as a set of Hamilton's equations of motion, similar to more conventional classical molecular dynamics. However, this original Hamiltonian PBME sometimes suffers from a large deviation in accuracy especially in the long time limit. Here, we propose a non-Hamiltonian variant of PBME to improve its behavior especially in that limit. As a benchmark, we simulate spin-boson and photosynthetic model systems and find that it consistently outperforms the original PBME and its Ehrenfest style variant. We explain the source of this improvement by decomposing the components of the mapping Hamiltonian and by assessing the energy flow between the system and the bath. We discuss strengths and weaknesses of our scheme with a viewpoint of offering future prospects.
Center for Self-assembly and Complexity, Institute for Basic Science (IBS), Pohang 790-784, Korea and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea.
Hyun Woo
HW
Kim
Center for Self-assembly and Complexity, Institute for Basic Science (IBS), Pohang 790-784, Korea and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea.
Young Min
YM
Rhee
D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D008956:Models, Chemical; D011789:Quantum Theory; D013816:Thermodynamics