Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Languages: English
Types: Article
Subjects: Condensed Matter - Statistical Mechanics
We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, similar to v(mu n), where mu <1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrodinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasicontinuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] Y. G. Sinai, Theor. Probab. Appl., 27, 256 (1982).
    • [2] J.-P. Bouchaud, A. Comtet, A. Georges, and P. Le Doussal, Annals of Physics, 201, 285 (1990); J. P. Bouchaud and A. Georges, Phys. Rep., 195, 127 (1990).
    • [3] J. A. Aronovitz and D. R. Nelson, Phys. Rev. A, 30, 1948 (1984); D. S. Fisher, D. Friedan, Z. Qiu, S. J. Shenker, and S. H. Shenker, ibid., 31, 3841 (1985).
    • [4] V. E. Kravtsov, I. V. Lerner, and V. I. Yudson, Zh. Eksp. Teor. Fiz., 91, 569 (1986); Phys. Lett. A, 119, 203 (1986).
    • [5] B. L. Altshuler, JETP Lett., 41, 648 (1985); P. A. Lee and A. D. Stone, Phys. Rev. Lett., 55, 1622 (1985).
    • [6] H. Kesten, Physica A, 138, 299 (1986).
    • [7] D. A. Gorokhov and G. Blatter, Phys. Rev. B, 58, 213 (1998); D. S. Fisher, P. Le Doussal, and C. Monthus, Phys. Rev. Lett., 80, 3539 (1998); H. E. Castillo and P. Le Doussal, 86, 4859 (2001).
    • [8] S. N. Majumdar and A. Comtet, Phys. Rev. E, 66, 061105 (2002).
    • [9] V. Freilikher, M. Pustilnik, and I. Yurkevich, Phys. Rev. Lett., 73, 810 (1994); Phys. Rev. B, 50, 6017 (1994); I. V. Yurkevich and I. V. Lerner, Phys. Rev. Lett., 82, 5080 (1999).
    • [10] K. Furutsu, J. Res. Nat. Bur. Stand., 67D, 303 (1963); E. A. Novikov, Sov. Phys. JETP, 20, 1290 (1965).
    • [11] In proper dimensional variables, the thermal noise correlator is proportional to the bare (short-range) di usion coe cient, while the random-drift correlator to some constant characterizing the disorder strength.
    • [12] I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the theory of disordered systems (Wiley, New York, 1988).
    • [13] When Re r > 1=2, one would need to keep y +r 1 instead of y r in Eq. (18a) which is, however, beyond the accuracy of the derivation of Eqs. (17).
    • [14] J. Bernasconi and W. R. Schneider, in Fractals in Physics, edited by L. Pietronero and E. Tosatti (Elsevier, New York, 1986).
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article