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Extreme events in particle densities within disordered media are linked to stretching exponents. Hot spots in intensity profiles correlate with minima in stretching exponents, revealing a key relationship in weak scattering phenomena.

Keywords:
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Area of Science:

  • Physics
  • Statistical Mechanics
  • Wave Phenomena

Background:

  • Weak scattering in random disordered media is crucial for understanding various physical phenomena.
  • Extreme-event statistics in these systems are of significant scientific interest.
  • Non-relativistic particle motion in random potentials presents complex behavior.

Purpose of the Study:

  • To investigate the relationship between extreme events in particle densities and stretching exponents.
  • To identify the physical conditions under which this relationship holds.
  • To explore the applicability of these findings to other physical systems.

Main Methods:

  • Analysis of non-relativistic particle motion through a weakly correlated random potential.
  • Examination of particle density profiles and associated extreme events.
  • Calculation and analysis of stretching exponents.

Main Results:

  • A strong correlation was found between extreme events in particle densities and stretching exponents.
  • 'Hot spots' in the intensity profile correspond to minima in the stretching exponents.
  • This connection is robust for weak, correlated random potential distributions.

Conclusions:

  • The study establishes a fundamental link between extreme particle densities and stretching exponents in disordered media.
  • The findings are expected to be generalizable to various random potential distributions and physical contexts, including wave phenomena.
  • This research provides insights into the statistical behavior of waves and particles in disordered environments.