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 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.

12 pages, 8 figures

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Cited by in corpus (14)

• Comparing and contrasting nuclei and cold atomic gases
• Entropic measures of Rydberg-like harmonic states
• Entanglement in N-harmonium: bosons and fermions
• Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics
• Bound states of Dipolar Bosons in One-dimensional Systems
• Analytic solutions of topologically disjoint systems
• Virial expansion coefficients in the harmonic approximation
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Heisenberg and entropic uncertainty measures for large-dimensional harmonic systems
• Bound Chains of Tilted Dipoles in Layered Systems
• Thermodynamics of Dipolar Chain Systems
• Many-particle Systems in One Dimension in the Harmonic Approximation
• Partial Fermionization---Spectral Universality in 1D Repulsive Bose Gases
• Bose-like few-fermion systems