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Statistics of transmitted power in multichannel dissipative ergodic structures
Igor Rozhkov1, Yan V Fyodorov, Richard L Weaver
1Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Summary
Random matrix theory (RMT) reveals wave power transmission in ergodic systems. This study analyzes open and closed systems with dissipation, offering insights into wave dynamics.
Area of Science:
- Wave physics
- Statistical mechanics
- Quantum chaos
Background:
- Ergodic wave motion in complex systems is crucial for understanding energy transport.
- Characterizing wave power transmission requires advanced theoretical frameworks.
Purpose of the Study:
- To investigate the probability distribution and moments of transmitted wave power in systems with ergodic wave motion.
- To analyze both open multichannel systems and closed systems with local dissipation.
Main Methods:
- Application of random matrix theory (RMT).
- Utilized the exact supersymmetry method.
- Employed a simpler RMT eigenstatistics-based technique for closed nondissipative systems.
Main Results:
- Derived the probability distribution function and moments for wave power transmission.
- Results are applicable to open systems and closed systems with local dissipation.
- Confirmed analytical results for the supersymmetry method via numerical simulations.
Conclusions:
- The simpler RMT method is accurate for closed systems with uniform dissipation or many weak dampers.
- The study provides a robust theoretical framework for wave power transmission in complex systems.
- Findings contribute to the understanding of wave phenomena in disordered and dissipative environments.