AI Article Synopsis
- The study examines a particle’s random movement on a one-dimensional lattice where the jump lengths follow a power-law distribution.
- The focus is on how a spatially dependent distribution of traps (targets) affects the probability of the particle getting trapped.
- The researchers find that if the exponent of the jump length distribution (μ) is less than the exponent of the trap distribution (α), there’s a chance the particle may never get trapped, implying slow search times even in larger systems.
Article Abstract
We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ+1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x)∼x(-α) and we find that, as long as μ<α, there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
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| http://dx.doi.org/10.1103/PhysRevE.92.042156 | DOI Listing |
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