Diffusion Monte Carlo Method with Lattice Regularization

Introduction to the Diffusion Monte Carlo Method

A self–contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and ...

Lattice Monte Carlo Analyses of Thermal Diffusion in Laminar Flow

Lattice Monte Carlo methods are an excellent choice for the simulation of non-linear thermal diffusion problems. In this paper, and for the first time, Lattice Monte Carlo analysis is performed on thermal diffusion combined with convective heat transfer. Laminar flow of water modeled as an incompressible fluid inside a copper pipe with a constant surface temperature is considered. For the simul...

Lattice-switching Monte Carlo method for crystals of flexible molecules.

We discuss implementation of the lattice-switching Monte Carlo method (LSMC) as a binary sampling between two synchronized Markov chains exploring separated minima in the potential energy landscape. When expressed in this fashion, the generalization to more complex crystals is straightforward. We extend the LSMC method to a flexible model of linear alkanes, incorporating bond length and angle c...

The Simulation–Tabulation Method forClassical Diffusion Monte Carlo

Many important classes of problems in materials science and biotechnology require the solution of the Laplace or Poisson equation in disordered two-phase domains in which the phase interface is extensive and convoluted. Green’s function first-passage (GFFP) methods solve such problems efficiently by generalizing the “walk on spheres” (WOS) method to allow first-passage (FP) domains to be not ju...

The Monte-Carlo Method