Abstract:
Random walks in one-dimensional environments with an additional dynamical feedback-coupling is analyzed numerically. The feedback introduced via a generalized master equation is controlled by a memory kernel of strength λ the explicit form of which is motivated by arguments used in mode-coupling theories. Introducing several realizations of the feedback mechanism within the simulations we obtain for a negative memory term, λ <, superdiffusion in the long time limit while a positive memory leads to localization of the particle. The numerical simulations are in agreement with recent predictions based on renormalization group techniques. A slight modification of the model including an exponentially decaying memory term and some possible applications for glasses and supercooled liquids are suggested. The relation to the true self-avoiding is discussed.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received 16 September 1999 and Received in final form 27 December 1999
Rights and permissions
About this article
Cite this article
Schulz, B., Trimper, S. & Schulz, M. Random walks in one-dimensional environments with feedback-coupling. Eur. Phys. J. B 15, 499–505 (2000). https://doi.org/10.1007/s100510051152
Issue Date:
DOI: https://doi.org/10.1007/s100510051152