Directed particle diffusion under "burnt bridges" conditions - art. no. 011102

We study random walks on a one-dimensional lattice that contains weak conne ctions, so-called "bridges." Each time the walker crosses the bridge from t he left or attempts to cross it from the right, the bridge may be destroyed with probability p; this restricts the particle's motion and directs it. O ur model, which incorporates asymmetric aspects in an otherwise symmetric h opping mechanism. is very akin to "Brownian ratchets" and to front propagat ion in autocatalytic A +B--->2A reactions. The analysis of the model and Mo nte Carlo simulations show that for large p the velocity of the directed mo tion is extremely sensitive to the distribution of bridges, whereas for sma ll p the velocity can be understood based on a mean-field analysis. The sin gle-particle model advanced by us here allows an almost quantitative unders tanding of the front's position in the A+B-->2A many-particle reaction.