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Concentration-of-Measure Theory for Structures and Fluctuations of Waves
Ping Fang1,2, Liyi Zhao1, Chushun Tian2
1Institute for Advanced Study, Tsinghua University, Beijing 100084,China.
Physical Review Letters
|October 20, 2018
Summary
This study introduces a new theory for wave phenomena in disordered media. It reveals a novel universality in wave-to-wave fluctuations, offering new perspectives on nonequilibrium statistical physics in open systems.
Area of Science:
- Complex wave systems
- Disordered media physics
- Statistical mechanics
Background:
- Understanding nonequilibrium phenomena in complex wave systems is crucial.
- Analytical studies of these systems are challenging.
Purpose of the Study:
- To develop a theory for wave structures and fluctuations in disordered media.
- To investigate wave-to-wave fluctuations and their universality.
- To establish criteria for stationary scattering states and their properties.
Main Methods:
- Utilized the mathematical tool of concentration of measure.
- Analyzed structures and fluctuations of waves in disordered media.
- Investigated transmission eigenchannels and their coherence.
Main Results:
- Discovered a new universality in wave-to-wave fluctuations, distinct from sample-to-sample fluctuations.
- Established a criterion for stationary scattering states to exhibit uniform spatial structure.
- Demonstrated that observable expectations are independent of incoming waves.
Conclusions:
- Wave-to-wave fluctuations offer new insights into mesoscopic phenomena.
- The findings suggest extending thermalization studies from closed to open systems.
- This work provides new perspectives on the emergence of nonequilibrium statistical phenomena.
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