The statistical error of Green's function Monte Carlo
The statistical error in the ground state energy as calculated by Green's Function Monte Carlo (GFMC) is analyzed and a simple approximate formula is derived which relates the error to the number of steps of the random walk, the variational energy of the trial function, and the time step of the random walk. Using this formula it is argued that as the thermodynamic limit is approached with N identical molecules, the computer time needed to reach a given error per molecule increases as N/sup n/ where 0.5 < b < 1.5 and as the nuclear charge Z of a system is increased the computer time necessary to reach a given error grows as Z/sup 5.5/. Thus GFMC simulations will be most useful for calculating the properties of low Z elements. The implications for choosing the optimal trial function from a series of trial functions is also discussed.
- Research Organization:
- Univ. di Trento, Povo
- OSTI ID:
- 6957495
- Report Number(s):
- CONF-8509213-
- Journal Information:
- J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 43:5/6; ISSN JSTPB
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ATOMIC MODELS
BOSONS
COMPUTERIZED SIMULATION
DATA COVARIANCES
ELECTRONS
ELEMENTARY PARTICLES
ENERGY LEVELS
FERMIONS
FUNCTIONS
GREEN FUNCTION
GROUND STATES
LEPTONS
MATHEMATICAL MODELS
MECHANICS
MONTE CARLO METHOD
QUANTUM MECHANICS
RANDOMNESS
SIMULATION
STATISTICAL MECHANICS
THERMODYNAMICS