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Evanescent continuous-time random walks.

E Abad1, S B Yuste2, Katja Lindenberg3

  • 1Departamento de Física Aplicada, Centro Universitario de Mérida, Universidad de Extremadura, E-06800 Mérida, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

Evanescence impacts distinct sites visited by random walkers. The study analyzes how this process, occurring during jumps or at any time, affects walker behavior with different waiting time distributions.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Mathematical Modeling

Background:

  • Continuous-time random walks are fundamental models in various scientific fields.
  • Evanescence, or particle loss, introduces complexity to standard random walk dynamics.
  • Understanding these effects is crucial for modeling phenomena like radioactive decay or trapping processes.

Purpose of the Study:

  • To investigate the influence of evanescence on the number of distinct sites visited by a one-dimensional continuous-time random walker.
  • To differentiate the impact of evanescence occurring solely during jumps versus evanescence occurring at any time.
  • To analyze the effects of various waiting time distributions (exponential, long-tailed, ultraslow) on these processes.

Main Methods:

  • Theoretical analysis of continuous-time random walks with an evanescence process.
  • Distinction between two primary evanescence mechanisms: jump-concurrent and time-dependent.
  • Examination of three waiting time distributions: exponential, long-tailed, and ultraslow.

Main Results:

  • Evanescence significantly alters the number of distinct sites visited compared to standard random walks.
  • The timing of evanescence (during jumps vs. at any time) leads to distinct behavioral patterns.
  • The nature of the waiting time distribution critically influences the walker's exploration capabilities under evanescence.

Conclusions:

  • The study provides a detailed understanding of how evanescence modifies random walker behavior in one dimension.
  • The findings are applicable to diverse systems involving particle loss and random movement.
  • The interplay between evanescence timing and waiting time distributions offers new insights into complex stochastic systems.