# Exact numerical simulations of a one-dimensional trapped Bose gas

## Abstract

We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density-matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local-density approximation. The transition between temperature-dominated to quantum-dominated correlation is determined. It is shown that despite the presence of the harmonic trapping potential, first-order correlations display, over a large range, the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.

- Authors:

- Fachbereich Physik, Technische Universitaet, Kaiserslautern, D-67663 Kaiserslautern (Germany)

- Publication Date:

- OSTI Identifier:
- 20982055

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.021601; (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; APPROXIMATIONS; BOSE-EINSTEIN GAS; BOSONS; CORRELATIONS; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; FORECASTING; GROUND STATES; NUMERICAL ANALYSIS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; RENORMALIZATION; SIMULATION; TEMPERATURE RANGE 0065-0273 K; THREE-BODY PROBLEM; TRAPPING; TRAPS; WEAK INTERACTIONS

### Citation Formats

```
Schmidt, Bernd, and Fleischhauer, Michael.
```*Exact numerical simulations of a one-dimensional trapped Bose gas*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.021601.

```
Schmidt, Bernd, & Fleischhauer, Michael.
```*Exact numerical simulations of a one-dimensional trapped Bose gas*. United States. doi:10.1103/PHYSREVA.75.021601.

```
Schmidt, Bernd, and Fleischhauer, Michael. Thu .
"Exact numerical simulations of a one-dimensional trapped Bose gas". United States.
doi:10.1103/PHYSREVA.75.021601.
```

```
@article{osti_20982055,
```

title = {Exact numerical simulations of a one-dimensional trapped Bose gas},

author = {Schmidt, Bernd and Fleischhauer, Michael},

abstractNote = {We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density-matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local-density approximation. The transition between temperature-dominated to quantum-dominated correlation is determined. It is shown that despite the presence of the harmonic trapping potential, first-order correlations display, over a large range, the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.},

doi = {10.1103/PHYSREVA.75.021601},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}