Derivation of Euler equations from quantum and classical microscopic dynamics

  title={Derivation of Euler equations from quantum and classical microscopic dynamics},
  author={Amirali Hannani and François Huveneers},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • A. HannaniF. Huveneers
  • Published 14 September 2022
  • Physics, Mathematics
  • Journal of Physics A: Mathematical and Theoretical
We derive Euler equations from a Hamiltonian microscopic dynamics. The microscopic system is a one-dimensional disordered harmonic chain, and the dynamics is either quantum or classical. This chain is an Anderson insulator with a symmetry protected mode: thermal fluctuations are frozen while the low modes ensure the transport of elongation, momentum and mechanical energy, that evolve according to Euler equations in an hyperbolic scaling limit. In this paper, we strengthen considerably the… 

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  • Srednicki
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.