Feynman-Kac path integral approach for the energy spectrum of many boson systems

TL;DR

This paper employs the Feynman-Kac path integral method to accurately analyze the ground and excited states of weakly interacting Bose gases, providing a more straightforward alternative to mean field approaches.

Contribution

It introduces a Feynman-Kac path integral approach for calculating energy spectra of many-boson systems, improving upon traditional mean field and Born approximation methods.

Findings

Method is exact in principle within numerical limits

Provides accurate energy spectra for Bose gases in dilute and dense regimes

Offers a simpler computational approach compared to Gross-Pitaevskii equation

Abstract

We study the ground and excited states of weakly interacting Bose gases (with positive and negative scattering lengths) in connection with Bose Einstein Condensation to test the validity of the mean field theory and Born approximation. They behave as new quantum fluids (a gas in the weak limit and a liquid in the dense limit and we study their many body physics in the dilute limit within the realistic potential model (Morse type) by Feynman-Kac path integral technique. Within numerical limitations, this method is exact in principle and turns out to be a better alternative to GP as all the ground and excited state properties can be calculated in a much simpler way.