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Observation and Analysis of Blinking Surface-enhanced Raman Scattering
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Splitting Probabilities of Symmetric Jump Processes.

J Klinger1,2, R Voituriez1,2, O Bénichou1

  • 1Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 4 Place Jussieu, 75005 Paris, France.

Physical Review Letters
|October 14, 2022
PubMed
Summary
This summary is machine-generated.

We derived an exact formula for jump processes, revealing that microscopic details significantly impact transmission probability, unlike continuous models. This finding is crucial for understanding light scattering in complex materials.

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Area of Science:

  • Mathematical Physics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Continuous jump processes are fundamental in modeling various physical phenomena.
  • Understanding the probability of a process reaching one boundary before another is critical for predicting system behavior.
  • Existing models often simplify microscopic dynamics, potentially overlooking crucial effects.

Purpose of the Study:

  • To derive a universal, exact asymptotic form for the splitting probability in symmetric continuous jump processes.
  • To explicitly determine the transmission probability, highlighting the limitations of continuous limits.
  • To provide a quantitative tool for characterizing light scattering in heterogeneous media.

Main Methods:

  • Derivation of an exact asymptotic form for the splitting probability using mathematical analysis.
  • Analysis of the transmission probability in the limit of the starting position approaching zero.
  • Application and illustration using paradigmatic models of jump processes.

Main Results:

  • A universal, exact asymptotic form for the splitting probability is established.
  • The transmission probability is explicitly determined, contradicting the trivial prediction from continuous limits.
  • The importance of microscopic jump process properties is demonstrated.

Conclusions:

  • The derived formula offers a precise prediction for the splitting probability in continuous jump processes.
  • Microscopic dynamics play a vital role in transmission phenomena, necessitating their inclusion in models.
  • The results provide experimentally measurable predictions for light scattering in 3D heterogeneous media.