SPONTANEOUS SCALING EMERGENCE IN GENERIC STOCHASTIC SYSTEMS

Sorin Solomon () and Moshe Levy ()
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Sorin Solomon: Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel

International Journal of Modern Physics C (IJMPC), 1996, vol. 07, issue 05, 745-751

Abstract: We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom.While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction.The systems present power laws with exponents which in a wide range(α −2there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.

Keywords: Scaling Emergence; Dynamical and Stochastic Chaos; Spontaneous Symmetry Breaking; Order Parameters Far from Equilibrium; Universal Critical Exponents; Pareto–Levy Laws (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (13)

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DOI: 10.1142/S0129183196000624

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