Self-diffusion in simple models: Systems with long-range jumps

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Google Scholar
Research Projects
Organizational Units
Journal Issue
We review some exact results for the morion of a tagged particle in simple models. Then, we study the density dependence of the sill-diffusion coefficient D_(N)(ρ) in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set of N neighboring sites. We obtain positive upper and lower bounds on F_(N)(ρ) = N{(1 - ρ) - [D_(N)(ρ)/D_(N)(0)]}/[ρ(1 - ρ)] for ρ is an element of [0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest that FN becomes effectively independent of N for N greater than or equal to 20.
© 1997 Plenum Publishing Corporation. We thank C. Landim, S. Olla, M. S. Ripoll, and H. T. Yau for useful discussions. This work was supported by NSF Grant 92-13424 4-20946. R.B. was also supported by D.G.I.C. y T. (Spain), project PB94-0265.
UCM subjects
Unesco subjects
2213 Termodinámica
1. H. Spohn, Large Scale Dynamics of lnteracting Particles (Springer-Verlag, Berlin, 1991 ); J. L. Lebowitz and H. Spohn, J. Stat. Phys, 28:539 ( 1982). 2. J. Quastel, Commun. Pure Appl. Math. 40:623-679 (1992). 3. F. Spitzer, J. Math. Mech. 18:973 (1968). 4. D. Durr, S. Goldstein, and J. L. Lebowitz, Phys. Rev. Lett. 57:1986; Commun. Pure Appl. Math. 38:573 (1985). 5. J. L. Lebowitz, J. Percus, and J. Sykes, Phys. Rev. 188:487 (1969): J, L. Lebowitz and J. Sykes, J. Stat. Ph. 6:157-171 (1974). 6. C. Kipnis and S. R. S. Varadhan, Commun. Math. Phys. 106:1-19 (1986): M. Z. Guo and G. Papanicolaou, in Proceedings Taniguchi Symposium (Kyoto, 1985). 7. A. de Masi, P. Ferrari, S. Goldstein, and D. Wick, J. Stat. Phys. 55:787-855 (1985). 8. R. Arratia, Ann. Prob. 11:362 373 (1983). 9. H. J. Bussemaker, J. Dufty, and M. Ernst, J. Stat. Phys. 78:1521 (1995): R. Esposito, R. Marra, and H. T. Yau, Rev. Math. Phys. 6:1233-1267 (1994). 10. R. Fernández, A. Sokal, and A, van Enter, J. Stat. Phys. 72:879-1167 (1993). 11. F. Spitzer, Adv. Math. 5:246-290 (1970). 12. E. Saada, Ann. Inst. H. Poincaré Prob. Stat. 26(1):5-17 (1990). 13. P. Siri, Ph.D. thesis, Torino (1996). 14. H. van Beijeren, J. Stat. Phys.60:845 (1990}. 15. S. R. S. Varadhan, Ann, Inst. H. Poincaré Prob. Stat. 31:273-285 (1995). 16. C. Kipnis, Ann. Prob. 14:397-408 (1986). 17. S. R. S. Varadhan and H. T. Yau, Private communication (1996). 18. S. R. S. Varadhan, Preprint (1993). 19. K. Kerr and K. Binder, in Application of the Monte Carlo Method in Statistical Physics (Berlin, Springer, 1984). 20. C. Landim, S. Olla, and S. B. Volchan, Preprint 96. 21. G. Giacomin and J. L. Lebowitz, Phys. Rev. Lett. 76:1094-1097 (1996}. 22. H. Spohn, J. Stat. Phys. 59:1227 (1990).