Many-particle Systems in One Dimension in the Harmonic Approximation

Abstract

We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic approximation scheme at the level of the Hamiltonian. We investigate the scaling with particle number of the ground state energies for systems consisting of identical bosons or fermions. We then proceed to focus on bosonic systems and make a detailed comparison to known exact results in the absence of the parabolic external trap for three-body systems. We also consider the thermodynamics of the harmonic model which turns out to be similar for bosons and fermions due to the lack of degeneracy in one dimension.

7+epsilon pages, 7 figures, published version

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Cited by in corpus (5)

• Comparing and contrasting nuclei and cold atomic gases
• Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• Bound states of Dipolar Bosons in One-dimensional Systems
• Five is More: Comments on Symmetry, Integrability, and Solvability for a Few Particles in a One-Dimensional Trap