title: Quantum statistics and thermodynamics in the harmonic approximation.
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.
authors.affiliation: Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark.
authors.forename: J R
authors.initials: JR
authors.lastname: Armstrong
authors.forename: N T
authors.initials: NT
authors.lastname: Zinner
authors.forename: D V
authors.initials: DV
authors.lastname: Fedorov
authors.forename: A S
authors.initials: AS
authors.lastname: Jensen
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D011789:Quantum Theory; D013816:Thermodynamics