First-principles quantum dynamics in interacting Bose gases I: The positive P representation

TL;DR

This paper evaluates the positive P representation for simulating quantum dynamics in interacting Bose gases, demonstrating its efficiency, accuracy, and suitability for open systems without truncation.

Contribution

It introduces and validates the positive P method for exact many-body quantum simulations of Bose gases, highlighting its scalability and advantages over other approaches.

Findings

Accurate simulation of correlation dynamics in 1D Bose gases.

Positive P method scales linearly with system size.

No truncation needed, suitable for open systems.

Abstract

The performance of the positive P phase-space representation for exact many-body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made to other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.