The Whitham approach to the c → 0 limit of the Lieb-Liniger model and generalized hydrodynamics

Research output: Contribution to journalArticlepeer-review


The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial conditions. A similarly powerful approach has recently emerged that is applicable to quantum integrable systems, namely the generalized hydrodynamics approach. This paper aims at showing that the Whitham approach is the semiclassical limit of the generalized hydrodynamics approach by connecting the two formal methods explicitly on the example of the Lieb-Liniger model on the quantum side to the non-linear Schrödinger equation on the classical side in the c → 0 limit, c being the interaction parameter. We show how quantum expectation values may be computed in this limit based on the connection established here which is mentioned above.

Original languageEnglish
Article number205204
JournalJournal of Physics A: Mathematical and Theoretical
Issue number20
StatePublished - 22 May 2020


  • Bethe ansatz
  • Lieb-Liniger model
  • Whitham theory
  • dispersionless limit
  • generalized hydrodynamics
  • nonlinear Schrödinger

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


Dive into the research topics of 'The Whitham approach to the c → 0 limit of the Lieb-Liniger model and generalized hydrodynamics'. Together they form a unique fingerprint.

Cite this