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From anomalous diffusion in polygons to a transport locking relation.

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Summary
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Particle transport in open channels exhibits faster-than-linear mean square displacement (MSD). A universal scaling law governs first return times, and transmission decays algebraically, revealing interdependent transport dynamics.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Particle transport in finite open channels is crucial for understanding complex systems.
  • Previous studies often focused on simpler geometries or infinite systems.

Purpose of the Study:

  • To investigate particle transport in finite-length open channels composed of connected polygonal billiards.
  • To analyze the scaling behavior of mean square displacement (MSD), first return times, and transmission probability.
  • To establish a relationship between these transport characteristics.

Main Methods:

  • Analysis of particle trajectories within polygonal billiard channels.
  • Derivation of scaling exponents for MSD and first return time distributions.
  • Calculation of the transmission coefficient as a function of system size.

Main Results:

  • The mean square displacement (MSD) grows faster than linearly with time.
  • First return time distributions exhibit algebraic decay with two distinct exponents and follow a scaling law.
  • Transmission coefficient decays algebraically with system size, indicating non-recurrent transport.

Conclusions:

  • A 'locking relation' connects the scaling exponents of MSD, first return times, and transmission decay.
  • This relation holds for various transport processes, including diffusive and fractional Brownian motion.
  • The findings suggest a universal framework for understanding transport in finite open systems.