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Above two dimensions, diffusion of a particle in a medium with quenchedrandom traps is believed to be well-described by the annealed continuous timerandom walk (CTRW). We propose an approximate expression for thefirst-passage-time (FPT) distribution in a given sample that enables detailedcomparison of the two problems. For a system of finite size, the number andspatial arrangement of deep traps yield significant sample-to-sample variationsin the FPT statistics. Numerical simulations of a quenched trap model withpower-law sojourn times confirm the existence of two characteristic time scalesand a non-self-averaging FPT distribution, as predicted by theory.

Sample-dependent first-passage time distribution in a disordered medium