Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption

Area of Science:

• Condensed matter physics
• Quantum chaos
• Wave scattering in disordered systems

Background:

• The reflection matrix (R=S†S) deviates from the unit matrix due to finite absorption in scattering systems.
• Understanding eigenvalue distributions is crucial for characterizing transport and statistical properties.

Purpose of the Study:

• To analytically derive the eigenvalue distribution function of the reflection matrix for chaotic cavities with finite absorption.
• To investigate the influence of system openness and time-reversal symmetry on this distribution.

Main Methods:

• Utilizing the random matrix approach.
• Calculating the eigenvalue distribution in the limit of many propagating modes in attached leads.
• Analyzing perfectly and weakly open cavity cases.

Main Results:

• An analytical expression for the reflection matrix eigenvalue distribution was obtained.
• The result is independent of time-reversal symmetry.
• The distribution is valid for finite absorption and arbitrary system openness.

Conclusions:

• The derived eigenvalue distribution provides a universal description for reflection in chaotic systems with absorption.
• This framework is applicable to systems ranging from perfectly to weakly open cavities.
• The findings have implications for understanding thermal emission from random media.