Equivalent Linear Two-Body Equations for Many-Body Systems

TL;DR

This paper introduces a variational method to derive equivalent linear two-body equations for many-boson systems, effectively simplifying complex N-body problems and providing accurate results for large N in various quantum systems.

Contribution

It presents a novel variational approach to obtain linear two-body equations for many-boson systems, applicable to contact interactions and Bose-Einstein condensates.

Findings

Accurately models large N bosonic systems

Effective for one-dimensional contact interactions

Provides excellent results for dilute BECs in traps

Abstract

A method has been developed for obtaining equivalent linear two-body equations (ELTBE) for the system of many ($N$) bosons using the variational principle. The method has been applied to the one-dimensional N-body problem with pair-wise contact interactions (McGurie-Yang N-body problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in anisotropic harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for large N.