# 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:

- Institute of Mathematics, University of Munich, Theresienstrasse 39, D-80333 Munich (Germany)
- Department of Mathematics, UC Davis, One Shields Avenue, Davis, California 95616 (United States)
- 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}

}

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