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Related Experiment Videos

Intermittent Kac's flights with resetting.

Manuel O Cáceres1,2, Marco Nizama3

  • 1Universidad Nacional de Cuyo, Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Avenida E. Bustillo 9500, CP8400 Bariloche, Argentina.

Physical Review. E
|February 20, 2026
PubMed
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This study explores an intermittent telegrapher equation with resetting, analyzing its diffusion-like process and mean first passage time. The research provides solutions for the evolution of distributions and their stationary states.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • The telegrapher equation models particle transport with switching velocities.
  • Intermittent velocity changes and resetting mechanisms introduce complex dynamics.
  • Kac's flights describe random walks with velocity reversals.

Purpose of the Study:

  • To analyze a generalized telegrapher equation with intermittent velocity sign changes and a resetting mechanism.
  • To derive solutions for the evolution of probability distributions and their stationary states.
  • To investigate the mean first passage time for this complex diffusion process.

Main Methods:

  • Utilized the fluctuation-dissipation theorem.
  • Developed a memory-like master equation approach.

Related Experiment Videos

  • Analyzed time-dependent propagators, stationary distributions, and variance as a function of resetting time.

    • Main Results:

    • Obtained solutions for the evolution of a normalized positive distribution, characterizing an intermittent hyperbolic diffusion-like process.
    • Studied the time-dependent propagator and its stationary distribution.
    • Investigated the variance and mean first passage time in the presence of resetting.

    Conclusions:

    • The study presents a novel approach to solving the intermittent telegrapher equation with resetting.
    • The findings offer insights into anomalous diffusion phenomena.
    • The framework allows for the analysis of limiting cases, including ordinary diffusion and telegrapher equations with resetting.