Statistics of wave functions in coupled chaotic systems

Area of Science:

• Quantum physics
• Condensed matter physics
• Statistical mechanics

Background:

• Disordered and chaotic quantum systems exhibit complex electron wave function behavior.
• Understanding spatial correlations in these systems is crucial for quantum transport phenomena.
• Previous studies often focused on single systems, limiting insights into coupled dynamics.

Purpose of the Study:

• To calculate the joint distribution of local electron wave function densities in two coupled quantum billiards.
• To identify and characterize spatial correlations arising from the coupling between quantum systems.
• To explore the universality of these correlations and their dependence on coupling details.

Main Methods:

• Application of the supersymmetry technique to analyze quantum chaotic systems.
• Exact calculation of the joint probability distribution of local densities.
• Analysis of electron wave functions in coupled disordered or chaotic quantum billiards.

Main Results:

• Discovery of novel spatial correlations in the joint distribution of local densities for coupled systems.
• These correlations are absent in single chaotic quantum billiards.
• The results demonstrate a universal behavior, independent of the microscopic coupling details.

Conclusions:

• The study provides an exact analytical solution for electron wave function correlations in coupled quantum billiards.
• The findings can be interpreted via the hybridization of eigenstates for weak coupling.
• The universality of the observed correlations has significant implications for understanding quantum transport in complex systems.