On the Dynamics of the Fermi-Bose Model

TL;DR

This paper introduces a computational method for analyzing the dynamics of the Fermi-Bose model in multiple dimensions, enabling efficient simulations of large and complex quantum systems such as molecular dissociation in 3D traps.

Contribution

It presents a novel approach using D-block-Hankel matrices to efficiently solve the system matrix for large-scale Fermi-Bose dynamics in arbitrary geometries.

Findings

Method effectively handles large dense systems

Applicable to three-dimensional physical systems

Numerical results demonstrate atomic pair correlations in 3D traps

Abstract

We consider the exponential matrix representing the dynamics of the Fermi-Bose model in an undepleted bosonic field approximation. A recent application of this model is molecular dimers dissociating into its atomic compounds. The problem is solved in D spatial dimensions by dividing the system matrix into blocks with generalizations of Hankel matrices, here refered to as D-block-Hankel matrices. The method is practically useful for treating large systems, i.e. dense computational grids or higher spatial dimensions, either on a single standard computer or a cluster. In particular the results can be used for studies of three-dimensional physical systems of arbitrary geometry. We illustrate the generality of our approach by giving numerical results for the dynamics of Glauber type atomic pair correlation functions for a non-isotropic three-dimensional harmonically trapped molecular Bose-Einstein condensate.