The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of disorder and traps yields a decreasing survival probability with broad distribution (log normal). Exact enumerations, effective-medium approximation, and spectral analysis are employed. This one-dimensional model shows rather rich behaviors which were previously believed to exist only in higher dimensionality. The possibility of a trapping-dominated super-universal-class is suggested.
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