# Nonperturbative dynamical many-body theory of a Bose-Einstein condensate

## Abstract

A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The nonperturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory, and 'off-shell' effects that are not captured by the Gross-Pitaevskii equation. This is relevant to account for the dynamics of, e.g., strongly interacting quantum gases atoms near a scattering resonance, or of one-dimensional Bose gases in the Tonks-Girardeau regime. We apply the theory to a homogeneous ultracold Bose gas in one spatial dimension. Considering the time evolution of an initial state far from equilibrium we show that it quickly evolves to a nonequilibrium quasistationary state and discuss the possibility to attribute an effective temperature to it. The approach to thermal equilibrium is found to be extremely slow.

- Authors:

- Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany)

- Publication Date:

- OSTI Identifier:
- 20786341

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063604; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ACTION INTEGRAL; APPROXIMATIONS; ATOMS; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; MANY-BODY PROBLEM; MEAN-FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; RESONANCE; SCATTERING; THERMAL EQUILIBRIUM

### Citation Formats

```
Gasenzer, Thomas, Berges, Juergen, Schmidt, Michael G., and Seco, Marcos.
```*Nonperturbative dynamical many-body theory of a Bose-Einstein condensate*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Gasenzer, Thomas, Berges, Juergen, Schmidt, Michael G., & Seco, Marcos.
```*Nonperturbative dynamical many-body theory of a Bose-Einstein condensate*. United States. doi:10.1103/PHYSREVA.72.0.

```
Gasenzer, Thomas, Berges, Juergen, Schmidt, Michael G., and Seco, Marcos. Thu .
"Nonperturbative dynamical many-body theory of a Bose-Einstein condensate". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786341,
```

title = {Nonperturbative dynamical many-body theory of a Bose-Einstein condensate},

author = {Gasenzer, Thomas and Berges, Juergen and Schmidt, Michael G. and Seco, Marcos},

abstractNote = {A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The nonperturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory, and 'off-shell' effects that are not captured by the Gross-Pitaevskii equation. This is relevant to account for the dynamics of, e.g., strongly interacting quantum gases atoms near a scattering resonance, or of one-dimensional Bose gases in the Tonks-Girardeau regime. We apply the theory to a homogeneous ultracold Bose gas in one spatial dimension. Considering the time evolution of an initial state far from equilibrium we show that it quickly evolves to a nonequilibrium quasistationary state and discuss the possibility to attribute an effective temperature to it. The approach to thermal equilibrium is found to be extremely slow.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 6,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}