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Macroscopic diffusion from a Hamilton-like dynamics

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Publication Date
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Hal-Diderot
Keywords
  • [Math.Math-Pr] Mathematics [Math]/Probability [Math.Pr]
  • [Nlin.Nlin-Cd] Nonlinear Sciences [Physics]/Chaotic Dynamics [Nlin.Cd]
  • [Phys.Cond.Cm-Sm] Physics [Physics]/Condensed Matter [Cond-Mat]/Statistical Mechanics [Cond-Mat.Stat
  • [Phys.Mphy] Physics [Physics]/Mathematical Physics [Math-Ph]
  • [Math.Math-Mp] Mathematics [Math]/Mathematical Physics [Math-Ph]
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Abstract

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model has all the properties of Hamiltonian dynamics in a confined phase space : it is deterministic, periodic, reversible and conservative. Randomness enters the model as a way to model ignorance about initial conditions and interactions between the components of the system. The orbits of the particles are non-intersecting random loops. We prove, as a weak law of large number, the validity of a diffusion equation for the macroscopic observables of interest for time arbitrary large, but small compared to the minimal recurrence time in the dynamics.

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