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
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.20.Dd – Kinetic theory / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000