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Percolation, sliding, localization and relaxation in topologically closed circuits
Daniel Hurowitz1, Doron Cohen1
1Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
Scientific Reports
|March 11, 2016
Summary
We studied random walks in random environments and found unique spectral properties distinct from non-hermitian systems. Our research identifies the threshold for under-damped relaxation and complexity saturation in biased systems.
Area of Science:
- Statistical physics
- Complex systems
Background:
- Random walks are fundamental models in statistical physics.
- Percolation and sliding transitions influence system dynamics.
- Non-hermitian Hamiltonians have been studied for eigenstate delocalization.
Purpose of the Study:
- To investigate relaxation modes of random walks in random environments.
- To compare spectral properties with non-hermitian systems.
- To determine the threshold for under-damped relaxation and observe complexity saturation.
Main Methods:
- Analysis of random walks on topologically closed circuits.
- Exploration of percolation and sliding transition effects.
- Investigation of spectral properties of conservative stochastic processes.
Main Results:
- Identified distinct spectral properties for conservative stochastic processes compared to non-hermitian systems.
- Determined the threshold for under-damped relaxation.
- Observed "complexity saturation" with increasing bias.
Conclusions:
- Conservative stochastic processes exhibit unique spectral behaviors.
- The study provides insights into relaxation dynamics and system complexity.
- Findings offer a new perspective on random walk dynamics in complex environments.
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