Abstract.
We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying energetic environment is also made dynamic by properly coupling the walker with the spin lattice. In fact, while the walker hops across nearest-neighbor sites, it can flip the pertaining spins, realizing a diffusive dynamics for the Ising system. As a result, the walk is biased towards high energy regions, namely the boundaries between clusters. Besides, the coupling introduced involves, with respect the ordinary diffusion laws, interesting corrections depending on either the temperature and the spin magnitude. In particular, they provide a further signature of the phase-transition occurring on the magnetic lattice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Avramov, A. Milchev, P. Argyrakis, Phys. Rev. E 47, 2303 (1993)
J. Bricmont, A. Kupiainen, Phys. Rev. Lett. 66, 1689 (1991)
A. Nitzan, M.A. Ratner, J. Phys. Chem. 98, 1765 (1994)
S. Bustingorry, E.R. Reyes, M.O. Cáceres, Phys. Rev. E 62, 7664 (2000)
A.K. Harrison, R. Zwanzig, Phys. Rev. A 32, 1072 (1985)
S.D. Druger, M.A. Ratner, A. Nitzan, Phys. Rev. B 31, 3939 (1985)
N. Masuda, N. Konno, Phys. Rev. E 69, 66113 (2004)
M. Slutsky, M. Kardar, L.A. Mirny, Phys. Rev. E 69, 61903 (2004)
B.D. Bookout, P.E. Parris, Phys. Rev. Lett. 71, 16 (1993)
I.A. Levitsky, Phys. Rev. B 49, 15594 (1994)
E. Arapaki, P. Argyrakis, I. Avramov, A. Milchev, Phys. Rev. E 56, 56 (1997)
W. Haus, K.W. Kehr, Phys. Rep. 150, 263 (1987)
B. Schulz, S. Trimper, M. Schulz, Eur. Phys. J. B 15, 499 (2000)
B. Schulz, S. Trimper, Phys. Lett. A 256, 266 (1999)
M. Schulz, S. Trimper, Phys. Rev. E 62, 221 (2000)
K. Sapag, V. Pereyra, J.L. Riccardo, G. Zgrablich, Surf. Sci. 295, 433 (1993)
E. Agliari, R. Burioni, D. Cassi, A. Vezzani, Eur. Phys. J. B 46, 109 (2005)
P. Buonsante, R. Burioni, D. Cassi, A. Vezzani, Phys. Rev. E 66, 36121 (2002), and references therein
E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)
G.H. Weiss, Aspects and Applications of the Random Walk (Elsevier Science, Amsterdam 1994)
H. Weiss, R.J. Rubin, Adv. Chem. Phys. 52, 363 (1983)
R. Burioni, D. Cassi, J. Phys. A 38, R45 (2005)
J. Jonasson, O. Schramm, ArXiv Mathematics e-prints arXiv:math/0002034 (2000)
A. Dembo, Y. Peres, J. Rosen, O. Zeitouni, ArXiv Mathematics e-prints arXiv:math/0107191 (2001)
A.M. Nemirovsky, H.O. Martin, M.D. Coutinho-Filho, Phys. Rev. A 41, 761 (1990)
S. Trimper, U.C. Täuber, G.M. Schütz, Phys. Rev. E 62, 6071 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Agliari, E., Burioni, R., Cassi, D. et al. Random walks interacting with evolving energy landscapes. Eur. Phys. J. B 48, 529–536 (2005). https://doi.org/10.1140/epjb/e2006-00015-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00015-3