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Particle diffusion Monte Carlo (PDMC)

Author

Listed:
  • Zarezadeh Zakarya

    (Department of Electronic Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133Rome, Italy)

  • Costantini Giovanni

    (Department of Electronic Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133Rome, Italy)

Abstract

General expressions for anisotropic particle diffusion Monte Carlo (PDMC) in a d-dimensional space are presented. The calculations of ground state energy of a helium atom for solving the many-body Schrödinger equation is carried out by the proposed method. The accuracy and stability of the results are discussed relative to other alternative methods, and our experimental results within the statistical errors agree with the quantum Monte Carlo methods. We also clarify the benefits of the proposed method by modeling the quantum probability density of a free particle in a plane (energy eigenfunctions). The proposed model represents a remarkable improvement in terms of performance, accuracy and computational time over standard MCMC method.

Suggested Citation

  • Zarezadeh Zakarya & Costantini Giovanni, 2019. "Particle diffusion Monte Carlo (PDMC)," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 121-130, June.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:2:p:121-130:n:5
    DOI: 10.1515/mcma-2019-2037
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    References listed on IDEAS

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    1. Wagner, Wolfgang, 2018. "A random walk model for the Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 138-148.
    2. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
    3. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
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