https://doi.org/10.1007/s100510070017
Self-quenched dynamics
1
Department of Theoretical Physics,
Institute of Physics, Budapest University of Technology,
Budafoki út 8, Budapest, 1111, Hungary
2
Department of Theoretical Physics, University of Oxford,
1 Keble Road, Oxford OX1 3NP, UK
3
Surface du Verre et Interfaces, UMR CNRS/Saint-Gobain,
39 Quai Lucien Lefranc, 93303 Aubervilliers Cedex, France
Corresponding author: a torok@planck.phy.bme.hu
Received:
8
August
2000
Published online: 15 December 2000
We introduce a model for the slow relaxation of an energy
landscape caused by its local interaction with a random walker whose
motion is dictated by the landscape itself. By choosing relevant
measures of time and potential this self-quenched dynamics can
be mapped on to the "True"Self-Avoiding Walk model. This
correspondence reveals that the average distance of the walker at time
t from its starting point is 
, where
for one dimension and 1/2 for all higher dimensions.
Furthermore, the evolution of the landscape is similar to that in
growth models with extremal dynamics.
PACS: 05.40.Fb – Random walks and Levy flights / 05.65.+b – Self-organized systems / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
