Rigorous Derivation of the Gross-Pitaevskii Equation

Journal Article · Fri Jan 26 04:00:00 EST 2007 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.98.040404· OSTI ID:20861629

Erdo''s, Laszlo ^[1]; Schlein, Benjamin ^[2]; Yau, H -T ^[3]

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1. Institute of Mathematics, University of Munich, Theresienstrasse 39, D-80333 Munich (Germany)
2. Department of Mathematics, UC Davis, One Shields Avenue, Davis, California 95616 (United States)
3. Department of Mathematics, Harvard University, One Oxford Street, Massachusetts 02138 (United States)

The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.

• OSTI ID: 20861629
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 4 Vol. 98; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
CORRELATIONS
MANY-BODY PROBLEM
SCHROEDINGER EQUATION
TIME DEPENDENCE
TRAPPING