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Springer eBooks

Diffusion Monte Carlo Method

Ryo Maezono

Published Nov 8, 2025• 0 citations
Publisher
DOI
10.1007/978-981-95-4134-8_3

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In this paper, a diffusion Monte Carlo (DMC) method to determine the ground state of a particle in a double well potential is presented. The DMC method uses displacements, creations and deletions of diffusers or walkers. The effects of double well parameters on the ground state are studied. For validation of our DMC method, a harmonic oscillator potential is used and the DMC method gives accurate results. In the double well potential, the DMC results has shown that the ground state energy increases as the depth of the double well increases.
In this paper we discuss various aspects of diffusion Monte Carlo methods using a fixed number of walkers. First, a rigorous proof of the divergence of pure diffusion Monte Carlo (PDMC) methods (DMC without branching in which the weights are carried along trajectories) is given. Second, a bias-free Monte Carlo method combining DMC and PDMC approaches, and based on a minimal stochastic reconfiguration of the population, is discussed. Finally, some illustrative calculations for a system of coupled quantum rotators are presented.