High-momentum tail in the Tonks gas under harmonic confinement

الأصل · EN

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.