Crossover from regular to irregular behavior in current flow through open billiards

Area of Science:

• Quantum physics
• Mesoscopic physics
• Chaos theory

Background:

• Understanding quantum chaos is crucial for predicting electron transport in nanostructures.
• Nodal and saddle points in wavefunctions are key features for analyzing quantum chaotic systems.
• Coherent electron transport in two-dimensional (2D) billiards provides a model for studying quantum phenomena.

Purpose of the Study:

• To identify and characterize signatures of quantum chaos in open 2D billiards.
• To analyze the distributions of nodal points, saddle points, and streamlines in integrable and chaotic billiards.
• To investigate how billiard geometry and lead configurations influence quantum transport and chaos.

Main Methods:

• Numerical evaluation of distribution functions for nearest neighbor nodal points.
• Analysis of distributions for nodal points with specific vorticity and saddle points.
• Modeling electron transport in rectangular and Sinai billiards with varying lead geometries.

Main Results:

• A generic form for nodal point distributions was found in open chaotic billiards with net current.
• Distributions of nodal and saddle points serve as reliable signatures of quantum chaos in open systems.
• Rectangular billiards with sharp leads show ordered nodal patterns, while flaring/rounding induces chaotic behavior; Sinai billiards exhibit complex, volatile streamlines.

Conclusions:

• The distributions of nodal and saddle points are robust indicators of quantum chaos in open systems.
• System geometry, particularly lead configuration, significantly impacts the transition from order to quantum chaos.
• The study provides a framework for detecting quantum chaos in electron transport through mesoscopic systems.