next up previous contents
Next: Time step Up: Systematic errors Previous: Systematic errors   Contents

Population of walkers

A key ingredient of the DMC algorithm is the branching process (3.29). The algorithm is exact, i.e. gives the exact ground-state energy of the system, in the limit of an infinite population of walkers. However it is necessary to understand how many walkers have to be used in practice to estimate the energy with a given value of accuracy [27]. In Fig. 3.2 we plot the energy for a given value of the density $na^3 = 10^{-4}$ as a function of the mean number of walkers. In all simulations carried out in this work we have used about one hundred walkers.

Figure 3.2: Hard-spheres at $na^3 = 10^{-4}$. Dependence of the energy on the size of the population of walkers.
\includegraphics[width=\textwidth]{Ewalker.eps}