The early years of quantum Monte Carlo (1): the ground state

Abstract

The first Monte Carlo simulation on a computer was performed at the initiative of John Von Neumann in the years 1947-48. It concerned the direct simulation of the fission reaction : many of the elementary steps, like, for example, the reactive events when a neutron collides with an Uranium nucleus, were modeled as stochastic processes and use was made of (pseudo-)random numbers to that effect. Von Neumann's simulation proposal was described in a letter written to the director of the theory division in Los Alamos, Dr. Richtmyer. The letter has been since declassified ; it is written with so 3 many details that one can figure out precisely what the computer is really doing. The simulation itself took several years to be performed, it involved several people, among whom John Von Neumann and his wife Klara, Nick Metropolis, Stan Ulam and a few others. It was performed on various computers, starting from the historic ENIAC, within a rapidly-evolving hardware architecture as well as programming technique: at some stage, it involved the creation of the storedprogram concept [Haigh, 2014].This work is well documented and has been already analyzed by Peter Galison [Galison, 1996] as symptomatic of the paradigm shift induced by the computer in the physical sciences (the so-called trading zone).Those years of post-war period were years of great intellectual freedom and creativity. It also led to the organisation of several scientific meetings where engineers, chemists, physicists and mathematicians would discuss the possibilities offered by the new electronic machines [Hurd,1985]. Among topics being discussed, the use of statistical sampling and probability theory to produce solutions to partial differential equations and integro-differential equations .