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Title: Rigorous Derivation of the Gross-Pitaevskii Equation

Abstract

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.

Authors:
 [1];  [2];  [3]
  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)
Publication Date:
OSTI Identifier:
20861629
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevLett.98.040404; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; CORRELATIONS; MANY-BODY PROBLEM; SCHROEDINGER EQUATION; TIME DEPENDENCE; TRAPPING

Citation Formats

Erdo''s, Laszlo, Schlein, Benjamin, and Yau, H.-T.. Rigorous Derivation of the Gross-Pitaevskii Equation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.040404.
Erdo''s, Laszlo, Schlein, Benjamin, & Yau, H.-T.. Rigorous Derivation of the Gross-Pitaevskii Equation. United States. doi:10.1103/PHYSREVLETT.98.040404.
Erdo''s, Laszlo, Schlein, Benjamin, and Yau, H.-T.. Fri . "Rigorous Derivation of the Gross-Pitaevskii Equation". United States. doi:10.1103/PHYSREVLETT.98.040404.
@article{osti_20861629,
title = {Rigorous Derivation of the Gross-Pitaevskii Equation},
author = {Erdo''s, Laszlo and Schlein, Benjamin and Yau, H.-T.},
abstractNote = {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.},
doi = {10.1103/PHYSREVLETT.98.040404},
journal = {Physical Review Letters},
number = 4,
volume = 98,
place = {United States},
year = {Fri Jan 26 00:00:00 EST 2007},
month = {Fri Jan 26 00:00:00 EST 2007}
}