Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-11-15
Phys. Rev. E 71, 046707 (2005)
Physics
Condensed Matter
Statistical Mechanics
14 pages, 3 figures; submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.71.046707
We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Levy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Levy-Ciesielski implementation of path integrals, and the fast sampling algorithm.
No associations
LandOfFree
On the efficient Monte Carlo implementation of path integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the efficient Monte Carlo implementation of path integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the efficient Monte Carlo implementation of path integrals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-39316