Thermodynamic behavior of a one-dimensional Bose gas at low temperature

Year: 2017

Authors: De Rosi G., Astrakharchik GE., Stringari S.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, Via Sommarive 14, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, Via Sommarive 14, I-38123 Povo, Italy; Univ Politecn Cataluna, Dept Fis, ES-08034 Barcelona, Spain.

Abstract: We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a nonmonotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures T, we demonstrate that the coefficient in T-2 expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weakly interacting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-ansatz equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in detail. At T = 0 we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.

Journal/Review: PHYSICAL REVIEW A

Volume: 96 (1)      Pages from: 13613-1  to: 13613-13

More Information: G.D.R. and S.S. would like to acknowledge fruitful and helpful discussions with L.P. Pitaevskii, C. Menotti, S. Giorgini, M. Di Liberto, and G. Bertaina. This work has been supported by European Research Council through the QGBE grant, by the QUIC grant of the Horizon2020 FET program, and by Provincia Autonoma di Trento (G.D.R. and S.S.). G.D.R. acknowledges the hospitality of the Computer Simulation in Condensed Matter Research Group of Universitat Politecnica de Catalunya in Barcelona, where this work was partially done. G.E.A. acknowledges partial financial support from the MICINN (Spain) Grant No. FIS2014-56257-C2-1-P. The Barcelona Supercomputing Center (The Spanish National Supercomputing Center-Centro Nacional de Supercomputacion) is acknowledged for the provided computational facilities. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ). The authors w ould like to acknowledge also G. Lang, X.-W. Guan, and the referees of this paper for useful comments and suggestions which have allowed some improvements in the revised version of this work.
KeyWords: Quantum; Bosons; System; Order
DOI: 10.1103/PhysRevA.96.013613

ImpactFactor: 2.909
Citations: 18
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