Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid

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Abstract

We analyze the probability distribution function (PDF) of work done on a Luttinger liquid for an arbitrary finite duration interaction quench and show that it can be described in terms of a generalized Gibbs ensemble. We construct the corresponding density matrix with explicit intermode correlations, and determine the duration and interaction dependence of the probability of an adiabatic transition and the PDF of nonadiabatic processes. In the thermodynamic limit, the PDF of work exhibits a non-Gaussian maximum around the excess heat, carrying almost all the spectral weight. In contrast, in the small system limit most spectral weight is carried by a delta peak at the energy of the adiabatic process, and an oscillating PDF with dips at energies commensurate to the quench duration and with an exponential envelope develops. Relevance to cold atom experiments is also discussed.

Original languageEnglish
Article number161109
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume86
Issue number16
DOIs
Publication statusPublished - okt. 22 2012

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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