Exact reformulation of the bosonic many-body problem in terms of stochastic wave functions: convergence issues

TL;DR

This paper analyzes different stochastic reformulations of the bosonic many-body problem, demonstrating that the simple Fock scheme uniquely ensures convergence in Monte Carlo simulations, unlike other schemes based on coherent states.

Contribution

The paper provides a simplified derivation of the simple Fock scheme and proves its convergence, highlighting its superiority over other stochastic schemes based on coherent states.

Findings

Simple Fock scheme converges in Monte Carlo simulations.

Other schemes based on coherent states lead to infinite statistical uncertainty.

The derivation of the simple Fock scheme is simplified compared to previous work.

Abstract

There exist methods to reformulate in an exact way the many-body problem of interacting bosons in terms of the stochastic evolution of single particle wave functions. For one such reformulation, the so-called simple Fock scheme, we present an elementary derivation, much simpler than the original one. Furthermore, we show that two other schemes, based on coherent states of the matter field rather than on Fock states, lead to an infinite statistical uncertainty in the continuous time limit. The simple Fock scheme is therefore, up to now, the only one that was proved to lead to a convergent Monte Carlo simulation scheme at all times.