Eur. Phys. J. B 15, 499-505 (2000)
https://doi.org/10.1007/s100510051152

Random walks in one-dimensional environments with feedback-coupling

Fachbereich Physik, Martin-Luther-Universität, 06099 Halle, Germany

Received: 16 September 1999
Revised: 27 December 1999
Published online: 15 June 2000

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, , 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.