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Setting Limits on Supersymmetry Using Simplified Models
07:46

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Published on: November 15, 2013

Weak subordination breaking for the quenched trap model.

S Burov1, E Barkai

  • 1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary

We introduce a novel mapping for diffusion in disordered systems, transforming it into Brownian motion. This method accurately predicts diffusion fronts and overcomes critical slowing down effects.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics

Background:

  • The quenched trap model describes diffusion in disordered media, presenting complex correlations.
  • Understanding diffusion dynamics in such systems is crucial for various physical phenomena.

Purpose of the Study:

  • To develop a new theoretical framework for analyzing diffusion in the quenched trap model.
  • To accurately predict the diffusion front and address limitations of existing models.

Main Methods:

  • Mapping the quenched trap model to Brownian motion terminated at a coverage time S(α).
  • Utilizing a Lévy time transformation to relate operational time S(α) to laboratory time t.
  • Analyzing Brownian motion stopped at S(α) to determine the diffusion front.

Main Results:

  • The developed mapping successfully predicts the diffusion front of the quenched trap model.
  • The zero-temperature limit (α→0) recovers established renormalization group solutions.
  • The theory effectively surmounts critical slowing down issues observed as α→1.

Conclusions:

  • The novel mapping provides a powerful tool for studying diffusion in disordered systems.
  • This approach offers a more tractable method for analyzing complex correlations in random walks.
  • The framework is particularly advantageous above the critical dimension of 2.