Dynamical critical exponent for two-species totally asymmetric diffusion on a ring

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Volumn 6, Issue , 2010, Pages

  Wehefritz Kaufmann, Birgit ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Asymmetric diffusion; Dynamical critical exponent; Nested Uq(SU(3)) Bethe ansatz

Indexed keywords

EID: 84860494218     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2010.039     Document Type: Article

References (46)

1. Ferrari P.A., Shocks in one-dimensional processes with a drift, in Probability and Phase Transition (Cambridge, UK, July 4-16, 1993), Editor G. Grimmett, NATO ASI Ser., Ser. C, Math. Phys. Sci., Vol. 420, Kluwer, Dordrecht, 1994, 35-48.
2. Ferrari P.A., Fontes L.R.G., Shock fluctuations in the asymmetric simple exclusion process, Probab. Theory Related Fields 99 (1994), 305-319.
3. Derrida B., Lebowitz J.L., Speer E.R., Shock profiles for the asymmetric simple exclusion process in one dimension, J. Stat. Phys. 89 (1997), 135-167 cond-mat/9708051.
4. Balázs M., Microscopic shape of shocks in a domain growth model, J. Stat. Phys. 105 (2001), 511-524 math.PR/0101124
5. Rákos A., Schütz G.M., Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities, J. Stat. Phys. 117 (2004), 55-76 cond-mat/0401461.
6. Bálazs M., Farkas G., Kovacs P., Rákos A., Random walk of second class particles in product shock measures, J. Stat. Phys. 139 (2010), 252-279 arXiv:0909.3071.
7. Jafarpour F.H., Multiple shocks in a driven diffusive system with two species of particles, Phys. A 358 (2005), 413-422 cond-mat/0504093.
8. Jafarpour F.H., Masharian S.R., The study of shocks in three-states driven-diffusive systems: a matrix product approach, J. Stat. Mech. Theory Exp. 2007 (2007), P03009, 18 pages, cond-mat/0612622.
9. Chowdhury A., Santen L., Schadschneider A., Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329 (2000), 199-329 cond-mat/0007053.
10. Macdonald J.T., Gibbs J.H., Pipkin A.C., Kinetics of biopolymerization on nucleic acid templates, Biopolymers 6 (1968), 1-25.
11. Schütz G., Non-equilibrium relaxation law for entangled polymers, Europhys. Lett. 48 (1999), 623-628.
12. Widom B., Viovy J.L., Defontaines A.D., Repton model of gel-electrophoresis and diffusion, J. Phys. I France 1 (1991), 1759-1784.
13. Dhar D., An exactly solved model for interfacial growth, Phase Transitions 9 (1987), 51-86.
14. de Gier J., Essler F., Exact spectral gaps of the asymmetric exclusion process with open boundaries, J. Stat. Mech. Theory Exp. 2006 (2006), P12011, 46 pages cond-mat/0609645.
15. Golinelli O., Mallick K., Derivation of a matrix product representation for the asymmetric exclusion process from algebraic Bethe ansatz, J. Phys. A: Math. Gen. 39 (2006), 10647-10658 cond-mat/0604338.
16. Gwa L.H., Spohn H., Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation, Phys. Rev. A 46 (1992), 844-854.
17. Schütz G.M., Exact solution of the master equation for the asymmetric exclusion process, J. Stat. Phys. 88 (1997), 427-445 cond-mat/9701019.
18. Angel O., The stationary measure of a 2-type totally asymmetric exclusion process, J. Combin. Theory Ser. A 113 (2006), 625-635 math.PR/0501005.
19. Evans M.R., Ferrari P.A., Mallick K., Matrix representation of the stationary mesure for the multispecies TASEP, J. Stat. Phys. 135 (2009), 217-239 arXiv:0807.0327.
20. Ferrari P.A., Martin J.B., Stationary distributions of multi-type totally asymmetric exclusion processes, Ann. Probab. 35 (2007), 807-832 math.PR/0501291.
21. Prolhac S., Evans M.R., Mallick K., The matrix product solution of the multispecies partially asymmetric exclusion process, J. Phys. A: Math. Theor. 42 (2009), 165004, 25 pages, arXiv:0812.3293.
22. Karimipour V., A multi-species asymmetric exclusion process, steady state and correlation functions on a periodic lattice, Europhys. Lett. 47 (1999), 304-310 cond-mat/9809193.
23. Jafarpour F.H., A two-species exclusion model with open boundaries: a use of q-deformed algebra, cond-mat/0004357.
24. Evans M.R., Foster D.P., Godreche C., Mukamel D., Asymmetric exclusion model with two species: spontaneous symmetry breaking, J. Stat. Phys. 80 (1995), 69-102.
25. Evans M.R., Foster D.P., Godreche C., Mukamel D., Spontaneous symmetry breaking in one dimensional driven diffusive system, Phys. Rev. Lett. 74 (1995), 208-211.
26. Ayyer A., Lebowitz J., Speer E.R., On the two species asymmetric exclusion process with semi-permeable boundaries, J. Stat. Phys. 135 (2009), 1009-1037, arXiv:0807.2423.
27. Uchiyama M., Two-species asymmetric exclusion process with open boundaries, Chaos Solitons Fractals 35 (2008), 398-407 cond-mat/0703660.
28. Arita C., Phase transitions in the two-species totally asymmetric exclusion process with boundaries, J. Stat. Mech. Theory Exp. 2006 (2006), P12008, 19 pages.
29. Kim K.H., den Nijs M., Dynamic screening in a two-species asymmetric exclusion process, Phys. Rev. E 76 (2007), 021107, 14 pages, arXiv:0705.1377.
30. Arndt P.F., Heinzel T., Rittenberg V., Spontaneous breaking of translational invariance and spatial condensation in stationary states on a ring. I. The neutral system, J. Stat. Phys. 97 (1999), 1-65 cond-mat/9809123.
31. Arita C., Kuniba A., Sakai K., Sawabe T., Spectrum in multi-species simple exclusion process on a ring, J. Phys. A: Math. Theor. 42 (2009), 345002, 41 pages, arXiv:0904.1481.
32. Dahmen S.R., Reaction-diffusion processes described by three-state quantum chains and integrability, J. Phys. A: Math. Gen. 28 (1995), 905-922 cond-mat/9405031.
33. Popkov V., Fouladvand M.E., Schütz G.M., A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains, J. Phys. A: Math. Gen. 35 (2002), 7187-7204 hep-th/0205169.
34. Cantini L., Algebraic Bethe ansatz for the two-species ASEP with different hopping rates, J. Phys. A: Math. Theor. 41 (2008), 095001, 16 pages, arXiv:0710.4083.
35. Prähofer M., Spohn H., Current fluctuations for the totally asymmetric simple exclusion process, in In and Out of Equilibrium (Mambucaba, 2000), Editor V. Sidoravicius, Progr. Probab., Vol. 51, Birkhäuser Boston, Boston, MA, 2002, 185-204 cond-mat/0101200
36. Bálazs M., Seppäläinen T., Exact connections between current fluctuations and the second class particle in a class of deposition models, J. Stat. Phys. 127 (2007), 431-455 math.PR/0608437.
37. Alcaraz F.C., Droz M., Henkel M., Rittenberg, V., Reaction-diffusion processes, critical dynamics and quantum chains, Ann. Physics 230 (1994), 250-302 hep-th/9302112.
38. Alcaraz F.C., Rittenberg, V., Reaction-diffusion processes as physical realizations of Hecke algebras, Phys. Lett. B 314 (1993), 377-380 hep-th/9306116.
39. Kardar M., Parisi G., Zhang Y.C., Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56 (1986), 889-892.
40. Wilkinson D.R., Edwards S.F., The surface statistics of a granular aggregate, Proc. Roy. Soc. London Ser. A 381 (1982), no. 1780, 33-51.
41. n+1 symmetric generalization of the XXZ model, Nuclear Phys. B 200 (1982), 266-280.
42. Alcaraz C., Lecture notes, unpublished.
43. de Vega H.J., Yang-Baxter algebras, integrable theories and quantum groups, Internat. J. Modern Phys. A 4 (1989), 2371-2463.
44. Bulirsch R., Stoer J., Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus, Numer. Math. 6 (1964), 413-427.
45. Christe P., Henkel M., Introduction to conformal invariance and its applications to critical phenomena, Lecture Notes in Physics, New Series m: Monographs, Vol. 16, Springer-Verlag, Berlin, 1993.
46. de Gier J., Essler F.H.L., Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries, J. Phys. A: Math. Theor. 41 (2008), 485002, 25 pages, arXiv:0806.3493.