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Abstract: We numerically study free expansion of a few Lieb-Liniger bosons, which areinitially in the ground state of an infinitely deep hard-wall trap. Numericalcalculation is carried out by employing a standard Fourier transform, asfollows from the Fermi-Bose transformation for a time-dependent Lieb-Linigergas. We study the evolution of the momentum distribution, the real-spacesingle-particle density, and the occupancies of natural orbitals. Our numericalcalculation allows us to explore the behavior of these observables in thetransient regime of the expansion, where they are non-trivially affected by theparticle interactions. We derive analytically by using the stationary phaseapproximation the formula which connects the asymptotic shape of the momentumdistribution and the initial state. For sufficiently large times the momentumdistribution coincides up to a simple scaling transformation with the shapeof the real-space single-particle density the expansion is asymptoticallyballistic. Our analytical and numerical results are in good agreement.



Autor: D. Jukić, B. Klajn, H. Buljan

Fuente: https://arxiv.org/



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