# Stochastic simulation of a finite-temperature one-dimensional Bose gas: From the Bogoliubov to the Tonks-Girardeau regime

## Abstract

We present an ab initio stochastic method for calculating thermal properties of a trapped, one-dimensional Bose gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-type Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 20653241

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 71; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.71.041601; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN GAS; BOSONS; COMPARATIVE EVALUATIONS; CONVERGENCE; CORRELATIONS; DENSITY; DENSITY MATRIX; EVOLUTION; FACTORIZATION; FLUCTUATIONS; HAMILTONIANS; KINETIC ENERGY; ONE-DIMENSIONAL CALCULATIONS; RENORMALIZATION; SIMULATION; STOCHASTIC PROCESSES; STRONG INTERACTIONS; THERMODYNAMIC PROPERTIES; TRAPPING

### Citation Formats

```
Schmidt, B., Plimak, L.I., and Fleischhauer, M.
```*Stochastic simulation of a finite-temperature one-dimensional Bose gas: From the Bogoliubov to the Tonks-Girardeau regime*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevA.71.041601.

```
Schmidt, B., Plimak, L.I., & Fleischhauer, M.
```*Stochastic simulation of a finite-temperature one-dimensional Bose gas: From the Bogoliubov to the Tonks-Girardeau regime*. United States. doi:10.1103/PhysRevA.71.041601.

```
Schmidt, B., Plimak, L.I., and Fleischhauer, M. Fri .
"Stochastic simulation of a finite-temperature one-dimensional Bose gas: From the Bogoliubov to the Tonks-Girardeau regime". United States. doi:10.1103/PhysRevA.71.041601.
```

```
@article{osti_20653241,
```

title = {Stochastic simulation of a finite-temperature one-dimensional Bose gas: From the Bogoliubov to the Tonks-Girardeau regime},

author = {Schmidt, B. and Plimak, L.I. and Fleischhauer, M.},

abstractNote = {We present an ab initio stochastic method for calculating thermal properties of a trapped, one-dimensional Bose gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-type Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.},

doi = {10.1103/PhysRevA.71.041601},

journal = {Physical Review. A},

issn = {1050-2947},

number = 4,

volume = 71,

place = {United States},

year = {2005},

month = {4}

}

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