Wigner-Dyson statistics from the Keldysh sigma-model.

Area of Science:

• Condensed matter physics
• Quantum chaos

Background:

• Understanding the statistical properties of energy levels in disordered systems is crucial for characterizing quantum chaos.
• Metallic grains with broken time-reversal symmetry present a complex system for theoretical investigation.

Purpose of the Study:

• To determine the level statistics of disordered metallic grains with broken time-reversal invariance.
• To introduce and validate a novel theoretical approach for analyzing such systems.

Main Methods:

• Utilized the Keldysh nonlinear sigma-model framework.
• Employed a nonperturbative integration over all saddle points of the sigma-model manifold.

Main Results:

• Successfully obtained the level statistics for the specified disordered metallic grains.
• Demonstrated the efficacy of the nonperturbative saddle-point integration strategy.

Conclusions:

• The Keldysh nonlinear sigma-model provides a powerful tool for analyzing level statistics in disordered systems.
• The developed nonperturbative method is broadly applicable to problems involving disorder and interactions.