FRACTAL MEASURES OF MEAN 1ST PASSAGE TIME IN THE PRESENCE OF SINAI DISORDER

We consider mean first passage time (MFPT) of random walks from one en d to the other of a segment of a Sinai lattice, with a reflecting left boundary and an absorbing right boundary. Random fields are located a t each site and can accept values 1/2 +/- epsilon with equal probabili ty. We investigate the nature of the distribution of MFPT over Sinai f ields, employing multifractal formalism. We calculate the fractal dime nsion D(0) and find it varies nearly linearly with epsilon, the streng th of Sinai disorder. We then study the scaling behaviour of the parti tion function. To this end we make a scaling ansatz and fit it to our exact results on finite lattices, which yields the scaling exponents t au(q). We report results on the scaling exponents for various values o f the disorder parameter.