The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly interacting bosons we derive nonuniversal corrections to this equation of state taking into account finite-range effects of the interatomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the one-dimensional Bose gas thermodynamic quantities such as pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.
Finite-range corrections to the thermodynamics of the one-dimensional Bose gas
Cappellaro, A.;Salasnich, L.
2017
Abstract
The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly interacting bosons we derive nonuniversal corrections to this equation of state taking into account finite-range effects of the interatomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the one-dimensional Bose gas thermodynamic quantities such as pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.
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