Effective Linear Two-Body Method for Many-Body Problems

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.

28 pages

References in corpus (2)

• Macroscopic Quantum Tunneling of a Bose-Einstein Condensate with Attractive Interaction
• Stability of Solution of the Nonlinear Schrödinger Equation for the Bose-Einstein Condensation

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• The Hyperspherical Four-Fermion Problem
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• Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions
• Stability, effective dimensions, and interactions for bosons in deformed fields
• Separable Structure of Many-Body Ground-State Wave Function
• Orbital Variational Adiabatic Hyperspherical Method Applied to Bose-Einstein Condensates