MEANDERING MOSEYS

Random Walker gets less far than was anticipated on the basis of a Global Positioning System in which the map and compass were neglected: the mean squared displacement has decreased, and in other words, the diffusion constant of Random Walker is reduced. If, due to the presence of a large degree of disorder, the reduction due to GPS reaches the 100% level. Random Walker becomes stuck or, in more glorious terms, localized.

Space distribution for Random Walker

Walker function W (x, p), after number of steps, (a) N = 0 (b) N = 10, assuming initial wave packet as Gaussian exp (-x2/2), step size l = 0.05, f =2p and q = 2p/3.

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A function of d for the state of the quantum Random Walker after number of steps N = 0 (solid line) and N = 10 (dashed line).

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