The fast sampling algorithm for Lie-Trotter products

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.Comment: 4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies that have been repaired in the present version; A sample code implementing the algorithm for LJ clusters is available from the author upon reques

Low-noise high-voltage DC power supply for nanopositioning applications

Nanopositioning techniques currently applied to characterize physical properties of materials interesting for applications at the microscopic scale rely on high-voltage electronic control circuits that should have the lowest possible noise level. Here we introduce a simple, flexible, and custom-built power supply circuit that can provide +375\,V with a noise level below 10\,ppm. The flexibility of the circuit comes from its topology based on discrete MOSFET components that can be suitable replaced in order to change the polarity as well as the output voltage and current.Comment: 3 pages, 2 figure