Coping with the node problem in resonant scattering simulations using quantum trajectories: an efficient and accurate combined analytical-numerical scheme

We report an efficient approach to accurately and efficiently compute transmission probabilities in resonant deep tunneling regime. Dynamical systems subjects to this phenomenon prove hard to simulate numerically even with exact methods, which motivates new methodological developments owing to the impact resonant phenomena have in several processes such as chemical reactions and electronic transport. Our approach is based on the original reformulation of stationary quantum scattering as the propagation of a quantum trajectory in extended phase space. The present paper discusses in detail the node problem occurring to the time-independent quantum trajectory method in this very challenging situation, and introduces an efficient semi-analytical node-skipping scheme to circumvent expensive numerical integration in their vicinity. We illustrate how this numerical extension allows to treat all regimes of quantum tunneling with great versatility by comparison to existing approaches of the litterature. The quantum trajectory, thus, represents a very promising tool for the study of complex chemical reactions characterized by resonant tunneling effect