Quantum Statistics and Thermodynamics in the Harmonic Approximation

Details Quantum Statistics and Thermodynamics in the Harmonic Approximation Quantum Statistics and Thermodynamics in the Harmonic Approximation

2011-12-28

arxiv.org/abs/1112.6139v1

Phys. Rev. E 85, 021117 (2012)

Physics

Quantum Physics

12 pages, 8 figures

Scientific paper

10.1103/PhysRevE.85.021117

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 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 that is considerably more computationally intensive.

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