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Scaling behavior in a stochastic self-gravitating system.

N V Antonov1

  • 1Department of Theoretical Physics, St. Petersburg University, Uljanovskaja 1, St. Petersburg, Petrodvorez, 198504, Russia.

Physical Review Letters
|June 1, 2004
PubMed
Summary

This study reveals two large-scale scaling behaviors in self-gravitating matter using renormalization group methods. These behaviors are linked to stable fixed points, with rotational velocity components crucial for scaling laws.

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Area of Science:

  • Cosmology and astrophysics
  • Statistical physics

Background:

  • Classical self-gravitating matter systems exhibit complex dynamics.
  • Understanding large-scale structure formation requires analyzing scaling behaviors.

Purpose of the Study:

  • Investigate the scaling behavior of classical self-gravitating matter.
  • Identify and characterize different types of large-scale scaling laws.
  • Determine the role of velocity field components in scaling.

Main Methods:

  • Utilized a field theoretic renormalization group approach.
  • Analyzed a system of stochastic differential equations for velocity and density.
  • Calculated scaling dimensions using the one-loop approximation (epsilon expansion).

Main Results:

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  • Established the existence of two distinct large-scale scaling behaviors.
  • Identified stable, physically admissible fixed points of renormalization-group equations.
  • Found that velocity and density fields possess independent scaling dimensions.

Conclusions:

  • The rotational (nonpotential) components of the velocity field are critical for the formation of observed scaling laws.
  • The identified scaling behaviors and their stability regions provide insights into structure formation.
  • The renormalization group method offers a powerful tool for studying such complex systems.