Real-Time Diffusion Monte Carlo Method (Communications in Computational Physics, 2018)
Direct sampling of multi-dimensional systems with quantum Monte Carlomethods allows exact account of many-body effects or particle correlations. The moststraightforward approach to solve the Schrödinger equation, Diffusion Monte Carlo,has been used in several benchmark cases for other methods to pursue. Its robustnessis based on direct sampling of a positive probability density for diffusion in imaginarytime. It has been argued that the corresponding real time diffusion can not be realised,because the corresponding oscillating complex valued distribution can not be used todrive diffusion. Here, we demonstrate that this can be done by turning the distributionpiecewise positive and normalizable, and also, by using four types of walkers. Thisstudy is a proof of concept demonstration using the well-known and transparent case:one-dimensional harmonic oscillator. Furthermore, we show that our novel methodcan be used to find not only the ground state but also excited states and even the timeevolution of a given wave function. Considering fermionic systems, this method mayturn out to be feasible for finding the wave function nodes for other approaches.
Keywords: Path integral; quantum dynamics; first-principles; Monte Carlo; real-time.