DMC

An implementation of the Diffusion Monte Carlo method (DMC) for calculating the ground-state energy and wave function of a quantum system. This code is based on the algorithm described in Ref. [1].

Compilation

This program relies on the C++ functionality only present in C++11 or newer. Notably it makes use of the STL thread library. The code can be compiled with a command of the form

g++ -O3 -pthread dmc.cpp -o dmc

or the equivalent for your compiler of choice.

Running

DMC calculations may be run by passing appropriate arguments to the template function

template< int maxN, int dp >
void runSimulation( const int pNum, const int N0, const int nb, const double xmin, const double xmax,
                    const double timeStep, const double relaxTime, const double alpha,
                    std::array<double, dp> &x0, std::function<double (std::array<double, dp> &)> &V,
                    const int numThreads = 1, const bool printWF = false, const bool printDist = false )

The parameters are:

-maxN: The maximum number of points in the distribution.

-dp: The effective dimension of the problem, the number of particles multiplied by the spatial dimension.

-pNum: The number of particles.

-N0: The initial number of points in the distribution.

-nb: The number of buckets used for determining the wave function.

-xmin and xmax: Defines the support of the wave function [xmin,xmax]^dp.

-timeStep: The time step in atomic units.

-alpha: Update parameter for the self consistent energy calculation.

-x0: The initial position of all points in the distribution.

-V: The potential.

-numThreads: The number of concurrent simulations run.

-printWF: A boolean flag that controls output of the wave function

-printDist: A boolean flag that controls output of the distribution of points.

Two other functions that may be of interest to the user are

double uniform( const double a, const double b)

double gaussian( const double mean, const double stdDev)

which can be used to generate random numbers drawn from uniform/Gaussian distributions. These may be useful for generating initial values for x0.

The sample parameters provided in dmc.cpp will calculate the ground state of the quantum harmonic oscillator.

References

[1] I. Kosztin, B. Faber, and K. Schulten, Introduction to the Diffusion Monte Carlo Method. arXiv:physics/9702023 [physics.comp-ph].