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Wigner time-delay distribution in chaotic cavities and freezing transition
Christophe Texier1, Satya N Majumdar
1Université Paris Sud, CNRS, LPTMS, UMR 8626, Bâtiment 100, Orsay F-91405, France.
Physical Review Letters
|July 9, 2013
Summary
Researchers analyzed Wigner time delay distributions in chaotic cavities using a Coulomb gas method. They found power law tails arise from narrow resonances linked to a Coulomb gas freezing transition.
Area of Science:
- Quantum chaos
- Mesoscopic physics
- Statistical mechanics
Background:
- Understanding time delays in chaotic systems is crucial for quantum transport.
- Previous work established joint distributions for proper time delays in chaotic cavities.
Purpose of the Study:
- To derive the large deviation function for Wigner time delay distribution in the large N limit.
- To identify the physical mechanisms responsible for the observed power law tails.
Main Methods:
- Utilized the joint distribution for proper time delays of a chaotic cavity.
- Employed a Coulomb gas method in the limit of a large number of channels (N).
Main Results:
- Obtained the large deviation function for the Wigner time delay distribution.
- Demonstrated that power law tails originate from narrow resonance contributions.
- Linked these contributions to a second-order freezing transition in the Coulomb gas.
Conclusions:
- The Coulomb gas method provides a powerful tool for analyzing time delay distributions in chaotic systems.
- Narrow resonances and Coulomb gas freezing transitions are key to understanding non-universal behavior in Wigner time delays.
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