Anomalous transport in disordered dynamical systems (original) (raw)
Abstract
... transport properties such as the total suppression of chaotic diffusion and anomalous drift. The relation to random walks in random environments, in particular to the Sinai model, explains also the occurrence of ageing in such dynamical systems. Anomalous transport is ...
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
References (66)
- H.G. Schuster, Deterministic Chaos, 3rd augm. ed., VCH, Weinheim, 1995.
- E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993.
- J.R. Dorfman, An Introduction to Chaos in Nonequi- librium Statistical Mechanics, Cambridge University Press, Cambridge, 1999.
- P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge University Press, Cambridge, 1998.
- M. Mezard, G. Parisi, M.A. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore, 1987.
- H. van Beijeren, J.R. Dorfman, Phys. Rev. Lett. 74 (1995) 4412.
- D. Weiss, et al., Phys. Rev. Lett. 66 (1991) 2790.
- R. Fleischmann, T. Geisel, R. Ketzmerick, Phys. Rev. Lett. 68 (1992) 1367.
- T. Geisel, A. Zacherl, G. Radons, Phys. Rev. Lett. 59 (1987) 2503.
- T. Geisel, J. Nierwetberg, Phys. Rev. Lett. 48 (1982) 7.
- S. Grossmann, H. Fujisaka, Phys. Rev. A 26 (1982) 1779.
- H. Fujisaka, S. Grossmann, Z. Phys. B 48 (1982) 261.
- M. Schell, S. Fraser, R. Kapral, Phys. Rev. A 26 (1982) 504.
- T. Geisel, S. Thomae, Phys. Rev. Lett. 52 (1984) 1936.
- T. Geisel, J. Nierwetberg, A. Zacherl, Phys. Rev. Lett. 54 (1985) 616.
- R. Artuso, Phys. Lett. A 202 (1992) 195.
- G. Zumofen, J. Klafter, Phys. Rev. E 47 (1993) 851.
- X.-J. Wang, C.-K. Hu, Phys. Rev. E 48 (1993) 728.
- R. Artuso, Casati, R. Lombardi, Phys. Rev. Lett. 71 (1993) 62.
- R. Stoop, Phys. Rev. E 49 (1994) 4913.
- R. Klages, J.R. Dorfman, Phys. Rev. Lett. 74 (1995) 387.
- G. Radons, Phys. Rep. 290 (1997) 67.
- C. Beck, F. Schlögl, Thermodynamics of Chaotic Systems, Cambridge University Press, Cambridge, 1993.
- J.-P. Bouchaud, A. Georges, Phys. Rep. 195 (1990) 127.
- Ya.G. Sinai, Theor. Prob. Appl. 27 (1982) 247.
- A. Golosov, Commun. Math. Phys. 92 (1984) 491.
- B.D. Hughes, Random Walks and Random Environments, vol. 2: Random Environments, Clarendon Press, Oxford, Chapter 6, 1996.
- G. Radons, Phys. Rev. Lett. 77 (1996) 4748.
- G. Radons, Adv. Solid State Phys., Festkörperprobleme 38 (1999) 439.
- E. Hopf, Ergodentheorie, Springer, Berlin, 1937.
- B. Derrida, Y. Pomeau, Phys. Rev. Lett. 48 (1982) 627.
- B. Derrida, J. Stat. Phys. 31 (1983) 433.
- G. Radons, J. Phys. A 31 (1998) 4141.
- P. Jung, J.G. Kissner, P. Hänggi, Phys. Rev. Lett. 76 (1996) 3436.
- Th. Harms, R. Lipowsky, Phys. Rev. Lett. 79 (1997) 2895.
- E. Barkai, J. Klafter, Phys. Rev. Lett. 79 (1997) 2245.
- L. Lundgren, et al., Phys. Rev. Lett. 51 (1983) 911.
- L.C.E. Struik, Physical Aging in Amorphous Polymers and Other Materials, Elsevier, Amsterdam, 1978.
- M. Rubí, C. Pérez-Vicente (Eds.), Complex Behaviour in Glassy Systems, Springer, Berlin, 1997.
- J.P. Bouchaud, L.F. Cugliandulo, J. Kurchan, M. Mezard, in: A.P. Young (Ed.), Spin Glasses and Random Fields, World Scientific, Singapore, 1998, cond-mat/9702070.
- E. Vincent, et al., in: M. Rubí, C. Pérez-Vicente (Eds.), Complex Behaviour in Glassy Systems, p. 184, cond-mat/ 9607224.
- E. Marinari, G. Parisi, J. Phys. A 26 (1993) L1149.
- F. Ritort, Phys. Rev. Lett. 75 (1995) 1190.
- L. Laloux, P. Le Doussal, Phys. Rev. E 57 (1998) 6296.
- D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80 (1998) 3539.
- P. Le Doussal, C. Monthus, D.S. Fisher, Phys. Rev. E 59 (1999) 4795.
- L.F. Cugliandulo, J. Kurchan, G. Parisi, J. Phys. I France 4 (1994) 1641.
- E. Barkai, Phys. Rev. Lett. 90 (2003) 104101.
- J. Dräger, J. Klafter, Phys. Rev. Lett. 84 (2000) 5998.
- J. Chave, E. Guitter, J. Phys. A 32 (1999) 445.
- C. Monthus, P. Le Doussal, Phys. Rev. E 65 (2002) 066129.
- S.N. Majumdar, A. Comtet, Phys. Rev. E 66 (2002) 061105.
- C. Monthus, Localization properties of the anomalous diffusion phase x ∼ t µ in the directed trap model and in the Sinai diffusion with bias, cond-mat/0212212.
- C. Monthus, P. Le Doussal, Energy dynamics in the Sinai model, cond-mat/0206035.
- J. Heldstab, H. Thomas, T. Geisel, G. Radons, Z. Phys. B 50 (1983) 141.
- S. Grossmann, Z. Phys. B 57 (1984) 77.
- M. Bianucci, R. Manella, X. Fan, P. Grigolino, B.J. West, Phys. Rev. E 47 (1993) 1510.
- M. Bianucci, R. Manella, B.J. West, P. Grigolino, Phys. Rev. E 50 (1994) 2693.
- I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 6th ed., Academic Press, San Diego, 2000.
- I.M. Lifshits, S.A. Gredeskul, L.A. Pastur, Introduction to the Theory of Disordered Systems, Wiley, New York, 1988.
- H. Risken, The Fokker-Planck Equation, 3rd ed., Springer, Berlin, 1996.
- J.P. Bouchaud, A. Comtet, A. Georges, P. Le Doussal, Europhys. Lett. 3 (1987) 653.
- T. Schneider, A. Politi, R. Badii, Phys. Rev. A 34 (1986) 2505.
- M. Nauenberg, J. Stat. Phys. 41 (1985) 803.
- S.H. Noskowicz, I. Goldhirsch, Phys. Rev. A 42 (1990) 2047.
- E.S. Key, Ann. Probab. 12 (1984) 529.