Quantum Monte Carlo using a Stochastic Poisson Solver

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Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually quantum Monte Carlo has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall quantum Monte Carlo scheme. We have developed a modified ''Walk ... continued below

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Das, D; Martin, R M & Kalos, M H May 6, 2005.

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Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually quantum Monte Carlo has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall quantum Monte Carlo scheme. We have developed a modified ''Walk On Spheres'' algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated within popular quantum Monte Carlo techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.

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PDF-file: 16 pages; size: 0.3 Mbytes

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  • Journal Name: Physical Review E; Journal Volume: 73; Journal Issue: 4

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  • Report No.: UCRL-JRNL-212119
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 883750
  • Archival Resource Key: ark:/67531/metadc873348

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  • May 6, 2005

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  • Sept. 21, 2016, 2:29 a.m.

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  • Nov. 30, 2016, 7:13 p.m.

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Das, D; Martin, R M & Kalos, M H. Quantum Monte Carlo using a Stochastic Poisson Solver, article, May 6, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc873348/: accessed August 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.