# Local density approximation for a perturbative equation of state

## Abstract

Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed.

- Authors:

- Dipartimento di Fisica, Universita di Trento and BEC-INFM, I-38050 Povo (Italy) and Institute of Spectroscopy, 142190 Troitsk (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20786357

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063620; (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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSONS; DENSITY; DENSITY FUNCTIONAL METHOD; EQUATIONS OF STATE; FERMI GAS; FERMIONS; GEOMETRY; INTEGRAL CALCULUS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; SERIES EXPANSION; SUM RULES; THOMAS-FERMI MODEL; TRAPPING

### Citation Formats

```
Astrakharchik, G. E.
```*Local density approximation for a perturbative equation of state*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Astrakharchik, G. E.
```*Local density approximation for a perturbative equation of state*. United States. doi:10.1103/PHYSREVA.72.0.

```
Astrakharchik, G. E. Thu .
"Local density approximation for a perturbative equation of state". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786357,
```

title = {Local density approximation for a perturbative equation of state},

author = {Astrakharchik, G. E.},

abstractNote = {Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed.},

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}

}