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Точные решения в неравновесной статистической механике

Точные решения в неравновесной статистической механике. В.Б. Приезжев ЛТФ ОИЯИ. Totally Asymmetric Exclusion Process. Totally Asymmetric Exclusion Process. Applications to: Hopping conductivity Queuing problems Directed polymers in random medium Traffic problems. Master Equation.

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Точные решения в неравновесной статистической механике

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  1. Точные решения в неравновесной статистической механике В.Б. ПриезжевЛТФ ОИЯИ

  2. Totally Asymmetric Exclusion Process

  3. Totally Asymmetric Exclusion Process • Applications to: • Hopping conductivity • Queuing problems • Directed polymers in random medium • Traffic problems

  4. Master Equation

  5. Substitution One-particle master equation (Poisson process) gives “Fourier ansatz ”

  6. We put

  7. From the initial conditions Poisson distribution

  8. Two-particle exclusion process then (2) has the form (1). Therefore, Eq.(1) + condition P(x,x)=P(x,x+1) gives the Asymmetric Exclusion Process

  9. As in the one-particle case, we have Bethe Ansatz

  10. From condition P(x,x)=P(x,x+1), we have

  11. From initial conditions Integrating, we obtain

  12. ASEP as a combinatorial problem

  13. Discrete formulation Free fermions TASEP

  14. of all free paths for time t.M.E. Fisher (1984):

  15. Cancellation for the TASEP (step 1) Reference coordinates for A,B,C,D

  16. Shift operators

  17. Cancellation for the TASEP (step 2)

  18. Solution for two particles

  19. General solution for infinite lattice

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