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Ray-Stretching Statistics and Hot-Spot Formation in Weak Random Disorder
1Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118, USA.
Entropy (Basel, Switzerland)
|January 21, 2023
Summary
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.
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.
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