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Real-Time Diffusion Monte Carlo Method

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Original languageEnglish
Pages (from-to)347-360
Number of pages14
JournalCommunications in Computational Physics
Issue number2
Publication statusPublished - Feb 2019
Publication typeA1 Journal article-refereed


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 Schrodinger 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 normalisable, 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.


  • Path integral, quantum dynamics, first-principles, Monte Carlo, real-time

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Field of science, Statistics Finland