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High-momentum tail in the Tonks gas under harmonic confinement

A. Minguzzi·P. Vignolo·M. P. Tosi
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Abstract

We use boson-fermion mapping to show that the single-particle momentum distribution in a one-dimensional gas of hard point-like bosons (Tonks gas) inside a harmonic trap decays as $p^{-4}$ at large momentum $p$. The relevant integrals expressing the one-body density matrix are evaluated for small numbers of particles in a simple Monte Carlo approach to test the extent of the asymptotic law and to illustrate the slow decay of correlations between the matter-wave field at different points.

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A. Minguzzi, P. Vignolo, M. P. Tosi. 2002-01-31. High-momentum tail in the Tonks gas under harmonic confinement. https://doi.org/10.1016/s0375-9601(02)00042-7

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