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High-momentum tail in the Tonks gas under harmonic confinement

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arxiv cond-mat/0201573 v1 pith:KPWB54P4 submitted 2002-01-31 cond-mat.stat-mech

High-momentum tail in the Tonks gas under harmonic confinement

classification cond-mat.stat-mech
keywords harmonicmomentumtonksapproachasymptoticboson-fermionbosonscarlo
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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