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We present a detailed comparison of the motion of a classical and of aquantum particle in the presence of trapping sites, within the framework ofcontinuous-time classical and quantum random walk. The main emphasis is on thequalitative differences in the temporal behavior of the survival probabilitiesof both kinds of particles. As a general rule, static traps are far lessefficient to absorb quantum particles than classical ones. Several latticegeometries are successively considered: an infinite chain with a single trap, afinite ring with a single trap, a finite ring with several traps, and aninfinite chain and a higher-dimensional lattice with a random distribution oftraps with a given density. For the latter disordered systems, the classicaland the quantum survival probabilities obey a stretched exponential asymptoticdecay, albeit with different exponents. These results confirm earlierpredictions, and the corresponding amplitudes are evaluated. In theone-dimensional geometry of the infinite chain, we obtain a full analyticalprediction for the amplitude of the quantum problem, including its dependenceon the trap density and strength.

Survival of classical and quantum particles in the presence of traps