# Stochastic method for calculating the ground state reduced density matrix of trapped Bose particles in one dimension

## TL;DR

This paper introduces a novel stochastic Monte Carlo method to compute the ground state reduced density matrix of trapped Bose particles in one dimension, addressing a challenging problem in quantum many-body physics.

## Contribution

The paper presents a new stochastic approach combining double-walker diffusion Monte Carlo with permanent calculation to evaluate the RDM for interacting bosons.

## Key findings

- Method demonstrates convergence on model systems.
- Provides insights into one-dimensional Bose systems.
- Applicable to various interaction strengths.

## Abstract

The reduced density matrix (RDM) is a fundamental contraction of the Bose-Einstein condensate wave function, encapsulating its one-body properties. It serves as a major analysis tool with which the condensed component of the density can be identified. Despite its cardinal importance, calculating the ground-state RDM of trapped interacting bosons is challenging and has been fully achieved only for specific models or when the pairwise interaction is weak. In this paper we discuss a new approach to compute the RDM based on a double-walker diffusion Monte Carlo random walk coupled with a stochastic permanent calculation. We here describe the new method and study some of its statistical convergence and properties applying it to some model systems.