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Phys. Rev. E 78, 061107 (2008) [12 pages]

Subdiffusive motion in kinetically constrained models

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Robert L. Jack
Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom and Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA

Peter Sollich
Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom

Peter Mayer
Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA

Received 18 September 2008; published 8 December 2008

We discuss a kinetically constrained model in which real-valued local densities fluctuate in time, as introduced recently by Bertin, Bouchaud, and Lequeux. We show how the phenomenology of this model can be reproduced by an effective theory of mobility excitations propagating in a disordered environment. Both excitations and probe particles have subdiffusive motion, characterized by different exponents and operating on different time scales. We derive these exponents, showing that they depend continuously on one of the parameters of the model.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.78.061107
DOI:
10.1103/PhysRevE.78.061107
PACS:
05.40.−a, 64.70.qd
 
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