1. Точные решения в неравновесной статистической механике В.Б. Приезжев ЛТФ ОИЯИ

2. Totally Asymmetric Exclusion Process

3. Applications to: 1.Hopping conductivity 2.Queuing problems 3.Directed polymers in random medium 4.Traffic problems

4. Master Equation

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

6. We put

7. From the initial conditions Poisson distribution

8. then (2) has the form (1). Therefore, Eq.(1) + condition P(x,x)=P(x,x+1) gives the Asymmetric Exclusion Process Two-particle 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. Integrating, we obtain From initial conditions

12. ASEP as a combinatorial problem

13. Free fermions TASEP Discrete formulation

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