Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons

Details Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons

1997-07-10

arxiv.org/abs/cond-mat/9707107v2

Physics

Condensed Matter

Statistical Mechanics

14 pages, 10 figures. The discussion on rescaling of the coupling is rewritten. Submitted to Phys. Rev. A

Scientific paper

10.1103/PhysRevA.57.3809

We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the ground state energy and density profile. We discuss the dependence of these quantities on both interaction strength g and particle number N. The ground state properties are compared to the predictions of the Gross-Pitaevskii equation, which depends on these parameters only through the combination Ng. We also calculate the specific heat based on the obtained energy spectra.

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