Effect of a tunnel barrier on time delay statistics

Area of Science:

• Quantum Chaos
• Quantum Transport
• Statistical Mechanics

Background:

• Understanding quantum chaotic systems is crucial for various fields.
• Time delay statistics provide insights into system dynamics.
• Tunnel barriers and broken time-reversal symmetry introduce complex behaviors.

Purpose of the Study:

• To develop a semiclassical approach for time delay statistics.
• To analyze systems with tunnel barriers and broken time-reversal symmetry.
• To derive and verify exact expressions for statistical moments.

Main Methods:

• Semiclassical approximation.
• Asymptotic series expansion in terms of barrier reflectivity.
• Conjecturing and numerical verification of exact expressions.

Main Results:

• Obtained asymptotic series for time delay statistics.
• Coefficients are rational functions of the channel number.
• Derived exact expressions for statistical moments, verified numerically.

Conclusions:

• The semiclassical approach provides accurate predictions for time delay statistics.
• The derived exact expressions are valid for arbitrary barrier reflectivity and channel number.
• Numerical verification supports the conjectured exact formulas.