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

Eldad Bettelheim*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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 languageAmerican English
Article number205204
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number20
DOIs
StatePublished - 22 May 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd.

Keywords

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

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