Effective Linear Two-Body Method for Many-Body Problems

TL;DR

This paper introduces an effective linear two-body approach for solving many-body problems, simplifying complex equations while maintaining high accuracy, demonstrated through applications to contact interactions and Bose-Einstein condensates.

Contribution

It presents a novel linear two-body method based on a variational principle for many-body problems, showing high accuracy for large N systems.

Findings

Accurately models one-dimensional N-body contact interactions

Effective for dilute Bose-Einstein condensates at zero temperature

Provides excellent results for large N systems

Abstract

This paper reports a detailed description of the equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. To test the accuracy of the method it 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 harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for large N.