Volume 98, Number 1, April 2012
|Number of page(s)||5|
|Published online||11 April 2012|
Exact equivalence between one-dimensional Bose gases interacting via hard-sphere and zero-range potentials
Lundbeck Foundation Theoretical Center for Quantum System Research, Department of Physics and Astronomy, Aarhus University - DK-8000 Aarhus C, Denmark, EU
Accepted: 9 March 2012
We prove the equivalence between the hard-sphere Bose gas and a system with momentum-dependent zero-range interactions in one spatial dimension, which we call extended hard-sphere Bose gas. The two-body interaction in the latter model has the advantage of being a regular pseudopotential. The most immediate consequence is the existence of its Fourier transform, permitting the formulation of the problem in momentum space, not possible with the original hard-core interaction. In addition, in the extended system, interactions are defined in terms of the scattering length, positive or negative, identified with the hard-sphere diameter only when it is positive. We are then able to obtain, directly in the thermodynamic limit, the ground-state energy of the strongly repulsive Lieb-Liniger gas and, more importantly, the energy of the lowest-lying super Tonks-Girardeau gas state with finite, strongly attractive interactions, in perturbation theory from the novel extended hard-sphere Bose gas.
PACS: 03.75.Hh – Static properties of condensates; thermodynamical, statistical, and structural properties / 05.30.Jp – Boson systems
© EPLA, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.