Integrating random matrix theory predictions with short-time dynamical effects in chaotic systems

Area of Science:

• Quantum chaos
• Statistical mechanics
• Random matrix theory

Background:

• Standard random matrix theory (RMT) describes universal statistical properties of energy levels in chaotic systems.
• Nonuniversal short-time dynamics often deviate from universal RMT predictions.
• Accurate analysis of chaotic systems requires incorporating these short-time effects.

Purpose of the Study:

• To develop a modified random matrix theory approach for eigenstate statistics.
• To systematically include nonuniversal short-time dynamics of chaotic systems.
• To provide a method that avoids computationally expensive Hamiltonian diagonalization.

Main Methods:

• Modification of random matrix theory (RMT) to incorporate short-time dynamics.
• Utilizing knowledge of short-time dynamics or classical approximations instead of full diagonalization.
• Analysis of wave-function autocorrelations and cross correlations.

Main Results:

• The modified method accurately captures eigenstate statistics by accounting for short-time behavior.
• Standard RMT and semiclassical predictions are recovered in appropriate limits (zero Ehrenfest time, infinite Heisenberg time).
• Significant accuracy improvements are demonstrated for chaotic systems compared to brute-force diagonalization.

Conclusions:

• The proposed method offers a more accurate and efficient approach to studying chaotic quantum systems.
• The technique remains accurate even when using classical approximations for short-time dynamics.
• Combining this method with correlation function bootstrapping further enhances convergence rates.