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Survival of classical and quantum particles in the presence of traps

Abstract : We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative differences in the temporal behavior of the survival probabilities of both kinds of particles. Several lattice geometries are successively considered: an infinite chain with a single trap, a finite ring with a single trap, a finite ring with several traps, and an infinite chain and a higher-dimensional lattice with a random distribution of traps with a given density. For the latter disordered systems, the classical and the quantum survival probabilities obey a stretched exponential asymptotic decay, albeit with different exponents. These results confirm earlier predictions, and the corresponding amplitudes are evaluated. In the one-dimensional geometry of the infinite chain, we obtain a full analytical prediction for the amplitude of the quantum problem, including its dependence on the trap density and strength.
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Submitted on : Wednesday, July 22, 2020 - 11:50:38 AM
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P. L. Krapivsky, J. M. Luck, K. Mallick. Survival of classical and quantum particles in the presence of traps. Journal of Statistical Physics, 2014, 154 (6), pp.1430-1460. ⟨10.1007/s10955-014-0936-8⟩. ⟨cea-00932075⟩



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