Physica A 287 (2000) 161–166 www.elsevier.com/locate/physa Intermittency in random maps R. Harish a ; ∗ , K.P.N. Murthy b a Reactor Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, TN, India b Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, TN, India Received 25 February 2000 Abstract The escape probability for a random walk on a one-dimensional lattice is discussed in terms of random maps. The global dynamics is found to be intermittent: the laminar regions with long sojourn near the upper xed point are broken by irregular bursts. Intermittency emerges even if the Sinai condition is not satised. It is shown that, if P is the probability of choosing the upper map, the average laminar length diverges as (1 − P) - . c  2000 Elsevier Science B.V. All rights reserved. PACS: 05.40.+j; 05.60.+w Over the past two decades, a great deal of eort has been devoted to the study of models based on random walks to study anomalous diusion in systems with quenched disorder [1–20]. Of interest is the Sinai lattice [10], where the mean square displacement of the diusing particle increases ultra-slowly as the fourth power of the logarithm of time. It is known that the mean rst passage time (MFPT), averaged over the Sinai disorder diverges with the system size L as exp(L). Recent study [21–23] has shown the possibility of casting the Sinai diusion problem in the language of iterated function system (IFS) [24]. In the IFS, two maps derived from the right and left jump probabilities p i and q i at site i on a one-dimensional lattice model the binary disorder satisfying the condition 〈ln(q=p)〉 = 0. It has been shown in these studies that the dynamical evolution exhibits intermittency: long sojourn near the upper xed point of the maps interrupted by irregular bursts. It has been conjectured [21] that for intermittency to be observed, two conditions have to be met: the two maps have to coincide at the upper xed point and the requirement of Sinai condition. In this * Corresponding author. E-mail address: harish@igcar.ernet.in (R. Harish). 0378-4371/00/$ - see front matter c  2000 Elsevier Science B.V. All rights reserved. PII: S0378-4371(00)00465-9