Perturbative correction to the ground state properties of one-dimensional strongly interacting bosons in a harmonic trap

Abstract

We calculate the first-order perturbation correction to the ground state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With $c$ denoting the interaction strength, we find that for a large number of particles $N$ the $1/c$ correction to the ground state energy increases as $N^{5/2}$, in contrast to the unperturbed Tonks-Girardeau value that is proportional to $N^2$. We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground state energy and reproduces the zero temperature thermodynamics obtained by a local density approximation.

5 pages, 3 PDF figures. Modifications to Fig. 1, experimental values. References added

References in corpus (5)

• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Density functional theory in one-dimension for contact-interacting fermions
• A density-functional approach to fermionization in the 1D Bose gas
• Designing potentials by sculpturing wires
• Lieb-Liniger gas in a constant force potential

Cited by in corpus (1)

• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases