Relaxation of Phonons in the Lieb-Liniger Gas by Dynamical Refermionization

Isabelle Bouchoule*, Jérôme Dubail, Léa Dubois, Dimitri M. Gangardt

*Corresponding author for this work

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Motivated by recent experiments, we investigate the Lieb-Liniger gas initially prepared in an out-of-equilibrium state that is Gaussian in terms of the phonons, namely whose density matrix is the exponential of an operator quadratic in terms of phonon creation and annihilation operators. Because the phonons are not exact eigenstates of the Hamiltonian, the gas relaxes to a stationary state at very long times whose phonon population is a priori different from the initial one. Thanks to integrability, that stationary state needs not be a thermal state. Using the Bethe-ansatz mapping between the exact eigenstates of the Lieb-Liniger Hamiltonian and those of a noninteracting Fermi gas and bosonization techniques we completely characterize the stationary state of the gas after relaxation and compute its phonon population distribution. We apply our results to the case where the initial state is an excited coherent state for a single phonon mode, and we compare them to exact results obtained in the hard-core limit.

Original languageEnglish
Article number140401
Number of pages6
JournalPhysical Review Letters
Issue number14
Early online date4 Apr 2023
Publication statusPublished - 7 Apr 2023

Bibliographical note

Funding Information:
We thank Jacopo de Nardis and Karol Kozlowski for very helpful discussions about Eq. and its relation to results on form factors in the literature. J. D. and D. M. G. acknowledge hospitality and support from Galileo Galilei Institute, Florence, Italy, during the program “Randomness, Integrability, and Universality”, where part of this work was done. This work was supported (I. B., J. D., L. D.) by the Agence Nationale de la Recherche Project QUADY–ANR-20-CE30-0017-01.

Publisher Copyright:
© 2023 American Physical Society.

ASJC Scopus subject areas

  • General Physics and Astronomy


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