Bosonizing one-dimensional cold atomic gases

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dc.creatorCazalilla, M. A.
dc.date2003-07-02
dc.date2003-10-30
dc.date.accessioned2026-07-07T02:52:09Z
dc.date.available2026-07-07T02:52:09Z
dc.descriptionWe present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as ``bosonization''), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method to compute the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Montecarlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.
dc.description39 pages + 14 EPS figures; typos corrected, references updated
dc.identifierhttps://arxiv.org/abs/cond-mat/0307033
dc.identifierhttp://arxiv.org/abs/cond-mat/0307033
dc.identifierJournal of Physics B: AMOP 37, S1-S47 (2004)
dc.identifierdoi:10.1088/0953-4075/37/7/051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/21733
dc.subjectMesoscale and Nanoscale Physics
dc.subjectStatistical Mechanics
dc.titleBosonizing one-dimensional cold atomic gases
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