Other sources of errors

Another type of error comes from the bias due to the trial wave function. For the quantities measured as pure estimators no effect was found. Also in the case of other estimators, such as the OBDM, the use of an optimized trial wavefunction yields reasonably small differences between mixed and variational estimators (less than $10\%$). In this case we believe that the extrapolated technique of section 3.3.4 gives reliable results. There is another source of error which arises from the hard-sphere model. In the DMC method the particles propagate according to diffusion (3.27) and drift (3.28) moves. Due to finite timestep it can happen during the simulation that some particle overlap with an impurity or another particle. This walker should not contribute to the calculation of averages because it does not satisfy the boundary conditions of the problem. One possibility is to artificially eliminate the walker or to redo the last diffusion jump so that it will choose another trajectory. Both of the choices bring in a systematic error. It is hard to investigate the effect of this error because it comes always mixed up with the timestep errors (3.4.2) and it is impossible to separate two effects. It is clear however that the percentage of the restarted or removed walkers must be kept small. For example in our calculations this percentage was always smaller than few percent.