Shift equivalence of measures and the intrinsic structure of shocks in the asymmetric simple exclusion process

Journal of Statistical Physics

Volumn 93, Issue 3-4, 1998, Pages 547-571

  Derrida, B ^a   Goldstein, S ^b   Lebowitz, J L ^b   Speer, E R ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Asymmetric simple exclusion process; Non translation invariant measures; Orbit coupling; Second class particles; Shift coupling; Shock structure

Indexed keywords

EID: 0039835344     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000033241.54615.43     Document Type: Article

References (30)

1. D. Ruelle, Statistical Mechanics: Rigorous Results (Benjamin, New York, 1969).
2. H.-O. Georgii, Gibbs Measures and Phase Transitions (Walter de Gruyter, Berlin, 1988).
3. R. Dobrushin, Gibbs states describing coexistence of phases for a three-dimensional Ising model, Th. Prob. Appl. 17:582-600 (1972).
4. G. Gallavotti, The phase separation line in the two-dimensional Ising model, Commun. Math. Phys. 27:103-136 (1972).
5. A. Messager and S. Miracle-Sole, Correlation functions and boundary conditions in the Ising ferromagnet, J. Stat. Phys. 17:245-262 (1977).
6. J. Bricmont, J. L. Lebowitz, and C. E. Pfister, On the local structure of the phase separation line in the two-dimensional Ising system, J. Stat. Phys. 26:313-332 (1981).
7. F. Spitzer, Interaction of Markov processes, Advances in Math. 5:246 290 (1970).
8. T. M. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985). See also references therein.
9. H. Rost, Nonequilibrium behavior of many particle process: density profiles and local equilibria, Z. Wahrsch. Verw. Gebiete 58:41-53 (1981).
10. E. D. Andjel and M. E. Vares, Hydrodynamical equations for attractive particle systems on ℤ, J. Stat. Phys. 47:265-288 (1987).
11. d, Commun. Math. Phys. 140:417-448 (1991).
12. E. D. Andjel, M. Bramson, and T. M. Liggett, Shocks in the asymmetric exclusion process, Probab. Theory Relat. Fields 78:231-247 (1988).
13. P. Ferrari and L. R. G. Fontes, Shock fluctuations in the asymmetric simple exclusion process, Probab. Theory Relat. Fields 99:305-319 (1994).
14. P. Ferrari, C. Kipnis, and E. Saada, Microscopic structure of traveling waves in the asymmetric simple exclusion, Ann. Probab. 19:226-244 (1991).
15. P. Ferrari, Shock fluctuations in asymmetric simple exclusion, Probab. Theory Relat. Fields 91:81-101 (1992).
16. B. Derrida, S. A. Janowsky, J. L. Lebowitz, and E. R. Speer, Exact solution of the totally asymmetric simple exclusion process: shock profiles, J. Stat. Phys. 73:813-842 (1993).
17. B. Derrida. J. L. Lebowitz, and E. R. Speer, Shock profiles in the asymmetric simple exclusion process in one dimension, J. Stat Phys. 89:135-167 (1997).
18. Work in preparation.
19. B. M. Gurevič and V. I. Oseledec, Gibbs distributions and dissipativeness of U-diffeomorphisms, Soviet Math. Dokl 14:570-573 (1973).
20. D. J. Aldous and H. Thorisson, Shift-coupling, Stoch. Proc. Appl. 44:1-14 (1993).
21. H. Thorisson, On time- and cycle-stationarity, Stoch. Proc. Appl. 55:183-209 (1995).
22. H.-O. Georgii, Orbit coupling, Ann. Inst. Henri Poincaré 33:253-268 (1997).
23. L. N. Vasershtein, Markov processes over denumerable products of spaces, describing large systems of automata, Problems Inform. Transmission 5:47-52 (1969).
24. S. Sandow, Partially asymmetric exclusion process with open boundaries, Phys. Rev. E 50:2660-2667 (1994).
25. S. Janowsky and J. L. Lebowitz, Finite size effects and shock fluctuations in the asymmetric simple exclusion process, Phys. Rev. A 45:618-625 (1992), and Exact results for the asymmetric simple exclusion process with a blockage, J. Stat Phys. 77:35-51 (1994).
26. S. Janowsky and J. L. Lebowitz, Finite size effects and shock fluctuations in the asymmetric simple exclusion process, Phys. Rev. A 45:618-625 (1992), and Exact results for the asymmetric simple exclusion process with a blockage, J. Stat Phys. 77:35-51 (1994).
27. B. Derrida, Systems out of equilibrium: some exactly solved models, in STATPHYS: the 19th IUPAP International Conference on Statistical Physics, H. Bailin, ed. (World Scientific, Singapore, 1996).
28. K. Mallick, Shocks in the asymmetric simple exclusion model with an impurity, J. Phys. A 29:5375-5386 (1996).
29. B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, An exact solution of a ID asymmetric exclusion model using a matrix formulation, J. Phys. A 26:1493-1517 (1993).
30. P. F. Arndt, T. Heinzel, and V. Rittenberg, First-order phase transitions in one-dimensional steady states, preprint SISSA Ref. 39/37/EP, cond-mat/9706114.