Exact equivalence between one-dimensional Bose gases interacting via hard-sphere and zero-range potentials

Manuel Valiente Cifuentes

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20 Citations (Scopus)

Abstract

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. Copyright (C) EPLA, 2012

Original languageEnglish
Article number10010
Number of pages5
JournalEurophysics Letters
Volume98
Issue number1
DOIs
Publication statusPublished - Apr 2012

Keywords

  • CORRELATED FERMI GAS
  • MANY-BODY PROBLEM
  • GROUND-STATE
  • SYSTEMS
  • BOSONS

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