TY - JOUR
T1 - Real-Time Diffusion Monte Carlo Method
AU - Ilkka Ruokosenmäki & Tapio T. Rantala
JO - Communications in Computational Physics
VL - 2
SP - 347
EP - 360
PY - 2018
DA - 2018/10
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2018-0048
UR - https://global-sci.org/intro/article_detail/cicp/12754.html
KW - Path integral, quantum dynamics, first-principles, Monte Carlo, real-time.
AB - <p style="text-align: justify;">Direct sampling of multi-dimensional systems with quantum Monte Carlo
methods allows exact account of many-body effects or particle correlations. The most
straightforward approach to solve the Schrödinger equation, Diffusion Monte Carlo,
has been used in several benchmark cases for other methods to pursue. Its robustness
is based on direct sampling of a positive probability density for diffusion in imaginary
time. 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 to
drive diffusion. Here, we demonstrate that this can be done by turning the distribution
piecewise positive and normalizable, and also, by using four types of walkers. This
study is a proof of concept demonstration using the well-known and transparent case:
one-dimensional harmonic oscillator. Furthermore, we show that our novel method
can be used to find not only the ground state but also excited states and even the time
evolution of a given wave function. Considering fermionic systems, this method may
turn out to be feasible for finding the wave function nodes for other approaches.</p>