Generalized microcanonical and Gibbs ensembles in classical and quantum integrable dynamics

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Abstract

We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it to the limit of infinite number of degrees of freedom. In quantum mechanics, we prove GGE for maximal Hamiltonians-a class of models stemming from a rigorous notion of quantum integrability understood as the existence of conserved charges with prescribed dependence on a system parameter, e.g. Hubbard U, anisotropy in the XXZ model etc. In analogy with classical integrability, the defining property of these models is that they have the maximum number of independent integrals. We contrast their dynamics induced by quenching the parameter to that of random matrix Hamiltonians.

Original languageEnglish (US)
Pages (from-to)288-296
Number of pages9
JournalAnnals of Physics
Volume367
DOIs
StatePublished - Apr 1 2016

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • Coherent many-body dynamics
  • Generalized Gibbs Ensemble
  • Integrable systems
  • Prethermalization
  • Quantum quenches
  • Statistical ensembles

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