Journal
PHYSICAL REVIEW A
Volume 96, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.96.013613
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Funding
- European Research Council through the QGBE grant
- QUIC grant of the Horizon FET program
- Provincia Autonoma di Trento
- MICINN (Spain) [FIS2014-56257-C2-1-P]
- Gauss Centre for Supercomputing e.V.
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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.
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