A generalized Lieb-Liniger model

Hagar Veksler, Shmuel Fishman

Research output: Contribution to journalArticlepeer-review


In 1963, Lieb and Liniger solved exactly a one-dimensional model of bosons interacting by a repulsive δ-potential and calculated the ground state in the thermodynamic limit. In the present work, we extend this model to a potential of three δ-functions - one of them is repulsive and the other two are attractive - modeling some aspects of the interaction between atoms, and we present an approximate solution for a dilute gas. In this limit, for low energy states, the results are found to be reduced to the ones of an effective Lieb-Liniger model with an effective δ-function of strength c eff and the regime of stability is identified. This may shed light on some aspects of interacting bosons.

Original languageEnglish
Article number085205
JournalJournal of Physics A: Mathematical and Theoretical
Issue number8
StatePublished - 20 Jan 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 IOP Publishing Ltd.


  • Bethe ansatz
  • LiebLiniger model
  • interacting bosons

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


Dive into the research topics of 'A generalized Lieb-Liniger model'. Together they form a unique fingerprint.

Cite this