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Statistics of reflection eigenvalues in chaotic cavities with nonideal leads
Pedro Vidal1, Eugene Kanzieper
1Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 58102, Israel.
Physical Review Letters
|September 26, 2012
Summary
This study uses the scattering matrix approach to find the probability density of reflection eigenvalues in chaotic cavities. The findings help analyze conductance fluctuations in quantum systems with broken time-reversal symmetry.
Area of Science:
- Quantum chaos
- Mesoscopic physics
- Condensed matter theory
Background:
- Understanding electron transport in chaotic cavities is crucial for quantum device development.
- The behavior of reflection eigenvalues governs transport properties.
- Broken time-reversal symmetry introduces unique phenomena in quantum systems.
Purpose of the Study:
- To determine the joint probability density function of reflection eigenvalues for chaotic cavities.
- To analyze the density and correlation functions of these eigenvalues.
- To investigate conductance fluctuations in asymmetric chaotic cavities.
Main Methods:
- Utilizing the scattering matrix approach.
- Assuming broken time-reversal symmetry.
- Calculating eigenvalue density and correlation functions.
Main Results:
- A novel joint probability density function for reflection eigenvalues was derived.
- The density and correlation functions of reflection eigenvalues were calculated.
- Fluctuations in Landauer conductance were analyzed for an asymmetric chaotic cavity.
Conclusions:
- The derived framework provides insights into quantum transport in chaotic systems.
- The results are applicable to understanding electron behavior in mesoscopic devices.
- Further theoretical extensions are identified for future research.
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