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We consider a particle moving in a one dimensional potential which has asymmetric deterministic part and a quenched random part. We study analyticallythe probability distributions of the local time (spent by the particle aroundits mean value) and the occupation time (spent above its mean value) within anobservation time window of size t. The random part of the potential is same asin the Sinai model, i.e., the potential itself is a random walk in space. Inthe absence of the random potential, these distributions have three typicalasymptotic behaviors depending on whether the deterministic potential isunstable, stable or flat. These asymptotic behaviors are shown to getdrastically modified when the random part of the potential is switched onleading to the loss of self-averaging and wide sample to sample fluctuations.Comment: 5 pages revtex, two column, minor typos correcte

Local and Occupation Time of a Particle Diffusing in a Random Medium