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Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Symmetric exclusion process with a localized source.

P L Krapivsky1

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

The total number of particles in a symmetric exclusion process grows with time, with distinct rates in 1D (√t), 2D (t/lnt), and higher dimensions. These growth patterns are independent of source intensity in 1D and 2D.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • Symmetric exclusion processes (SEPs) are fundamental models in statistical mechanics.
  • Understanding particle transport driven by localized sources is crucial for various physical systems.

Purpose of the Study:

  • To investigate the growth dynamics of the total number of particles in a 1D, 2D, and higher-dimensional SEP.
  • To analyze the influence of a localized source on particle accumulation.
  • To examine particle number fluctuations and variance in one dimension.

Main Methods:

  • Analytical investigation of the symmetric exclusion process.
  • Derivation of asymptotic behaviors for particle growth in different dimensions.
  • Analysis of particle number fluctuations and variance.

Main Results:

  • The average total number of particles grows as √t in 1D, t/lnt in 2D, and linearly in higher dimensions.
  • In 1D and 2D, the leading asymptotic growth is independent of the source intensity.
  • The asymptotic growth of the variance in the total number of particles is determined for 1D.

Conclusions:

  • The dimensionality of the system significantly dictates particle growth rates in SEPs driven by localized sources.
  • Source intensity does not affect the primary growth behavior in lower dimensions.
  • Fluctuations in particle number provide further insights into the system's dynamics.