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Tracer diffusion in lattice gases


It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds.

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Spohn, H. Tracer diffusion in lattice gases. J Stat Phys 59, 1227–1239 (1990).

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Key words

  • Stochastic lattice gases
  • self-diffusion
  • variational formula