### Abstract

We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center-of-mass motion, and by counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters, and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method, which is considerably more computationally intensive.

Original language | English (US) |
---|---|

Article number | 021117 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 85 |

Issue number | 2 |

DOIs | |

State | Published - Feb 10 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*85*(2), [021117]. https://doi.org/10.1103/PhysRevE.85.021117

**Quantum statistics and thermodynamics in the harmonic approximation.** / Armstrong, J. R.; Zinner, N. T.; Fedorov, D. V.; Jensen, A. S.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 85, no. 2, 021117. https://doi.org/10.1103/PhysRevE.85.021117

}

TY - JOUR

T1 - Quantum statistics and thermodynamics in the harmonic approximation

AU - Armstrong, J. R.

AU - Zinner, N. T.

AU - Fedorov, D. V.

AU - Jensen, A. S.

PY - 2012/2/10

Y1 - 2012/2/10

N2 - We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center-of-mass motion, and by counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters, and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method, which is considerably more computationally intensive.

AB - We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center-of-mass motion, and by counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters, and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method, which is considerably more computationally intensive.

UR - http://www.scopus.com/inward/record.url?scp=84857612877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857612877&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.85.021117

DO - 10.1103/PhysRevE.85.021117

M3 - Article

C2 - 22463163

AN - SCOPUS:84857612877

VL - 85

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 2

M1 - 021117

ER -