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First-encounter time of two diffusing particles in confinement.

F Le Vot1, S B Yuste1, E Abad2

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Summary
This summary is machine-generated.

Confinement significantly alters diffusion dynamics for two particles, impacting first-encounter times and survival probabilities. Boundary effects are crucial even in simple 1D systems.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Diffusion processes are fundamental in various scientific fields.
  • Understanding particle interactions in confined spaces is critical for kinetics.
  • First-encounter time and survival probability are key metrics in diffusion studies.

Purpose of the Study:

  • To investigate the impact of confinement on the first-encounter time and survival probability of two diffusing particles.
  • To derive analytical insights for one-dimensional diffusion in a half-line and an interval.
  • To explore the effects of equal and unequal particle diffusivities.

Main Methods:

  • Analytical treatment of diffusion in one-dimensional settings (half-line and interval).
  • Calculation of exact survival probability and first-encounter time density for equal diffusivities.
  • Evaluation of moments for the first-encounter time.
  • Analysis of long-time behavior of survival probability for unequal diffusivities.

Main Results:

  • Confinement drastically alters first-encounter time probability density and survival probability.
  • Exact analytical results for survival probability and first-encounter time density were obtained for equal diffusivities.
  • Moments of the first-encounter time were evaluated where they exist.
  • Long-time behavior of survival probability was analyzed for unequal diffusivities, highlighting boundary effect impacts.

Conclusions:

  • Boundary effects significantly influence diffusion-controlled kinetics, even in simple 1D systems.
  • Obtaining analytical results becomes challenging when translational invariance is broken.
  • The study provides a detailed understanding of confinement effects on particle diffusion dynamics.