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Autonomous models solvable through the full interval method

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Abstract

The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating function method, the general solution for F n , the probability that n consecutive sites be full, is obtained. Some other correlation functions of number operators at nonadjacent sites are also explicitly obtained. It is shown that for a special choice of initial conditions some correlation functions of number operators called full intervals remain uncorrelated.

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References

  1. G.M. Schütz, Exactly solvable models for many-body systems far from equilibrium, in Phase transitions and critical phenomena, edited by C. Domb, J. Lebowitz (Academic Press, 2000), Vol. 19

  2. M. Henkel, H. Hinrichsen, S. Lübeck, Non-equilibrium phase transitions, in Absorbing phase transitions (Springer, 2008), Vol. 1

  3. M. Henkel, M. Pleimling, Non-equilibrium phase transitions, in Ageing and Dynamical Scaling Far from Equilibrium (Springer, 2010), Vol. 2

  4. F.C. Alcaraz, M. Droz, M. Henkel, V. Rittenberg, Ann. Phys. 230, 250 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. K. Krebs, M.P. Pfannmüller, B. Wehefritz, H. Hinrichsen, J. Stat. Phys. 78, 1429 (1995)

    Article  ADS  MATH  Google Scholar 

  6. H. Simon, J. Phys. A 28, 6585 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. V. Privman, A.M.R. Cadilhe, M.L. Glasser, J. Stat. Phys. 81, 881 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. M. Henkel, E. Orlandini, G.M. Schütz, J. Phys. A 28, 6335 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. M. Henkel, E. Orlandini, J. Santos, Ann. Phys. 259, 163 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. A.A. Lushnikov, Sov. Phys. JETP 64, 81 (1986) [Zh. Eksp. Teor. Fiz. 91, 1376 (1986)]

    Google Scholar 

  11. M. Alimohammadi, V. Karimipour, M. Khorrami, Phys. Rev. E 57, 6370 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  12. M. Alimohammadi, V. Karimipour, M. Khorrami, J. Stat. Phys. 97, 373 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. A. Aghamohammadi, M. Khorrami, J. Phys. A 33, 7843 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. M.A. Burschka, C.R. Doering, D. Ben-Avraham, Phys. Rev. Lett. 63, 700 (1989)

    Article  ADS  Google Scholar 

  15. D. ben-Avraham, Mod. Phys. Lett. B 9, 895 (1995)

    Article  ADS  Google Scholar 

  16. D. ben-Avraham, in Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman (Cambridge University press, 1997), pp. 29–50

  17. D. ben-Avraham, Phys. Rev. Lett. 81, 4756 (1998)

    Article  ADS  Google Scholar 

  18. M. Henkel, H. Hinrichsen, J. Phys. A 34, 1561 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. T. Masser, D. ben-Avraham, Phys. Lett. A 275, 382 (2000)

    ADS  Google Scholar 

  20. M. Alimohammadi, M. Khorrami, A. Aghamohammadi, Phys. Rev. E 64, 056116 (2001)

    Article  ADS  Google Scholar 

  21. M. Khorrami, A. Aghamohammadi, M. Alimohammadi, J. Phys. A 36, 345 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. A. Aghamohammadi, M. Alimohammadi, M. Khorrami, Eur. Phys. J. B 31, 371 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  23. A. Aghamohammadi, M. Khorrami, Int. J. Mod. Phys. B 18, 204 (2004)

    Article  Google Scholar 

  24. A. Aghamohammadi, M. Khorrami, Eur. Phys. J. B 47, 583 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  25. M. Mobilia, P.A. Bares, Phys. Rev. E 64, 066123 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  26. X. Durang, J.-Y. Fortin, D. Del Biondo, M. Henkel, J. Richert, J. Stat. Mech., P04002 (2010)

  27. X. Durang, J.-Y. Fortin, M. Henkel, J. Stat. Mech., P02030 (2011)

  28. G.M. Schütz, J. Stat. Phys. 79, 243 (1995)

    Article  ADS  MATH  Google Scholar 

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Khorrami, M., Aghamohammadi, A. Autonomous models solvable through the full interval method. Eur. Phys. J. B 85, 134 (2012). https://doi.org/10.1140/epjb/e2012-20979-3

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  • DOI: https://doi.org/10.1140/epjb/e2012-20979-3

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