Lyapunov exponents in disordered chaotic systems: avoided crossing and level statistics

Area of Science:

• Nonlinear dynamics
• Quantum chaos
• Statistical physics

Background:

• Disordered systems exhibit complex behaviors.
• Lyapunov exponents quantify chaos in dynamical systems.
• Quantum chaos studies quantum systems with classical chaotic analogs.

Purpose of the Study:

• Investigate Lyapunov exponents in coupled chaotic maps.
• Compare their behavior to quantum energy levels.
• Explain observed phenomena using theoretical frameworks.

Main Methods:

• Studied disordered systems of mutually coupled chaotic maps.
• Analyzed the coupling dependence of Lyapunov exponents.
• Derived approximate expressions for Lyapunov exponent spacing distributions.

Main Results:

• Lyapunov exponents exhibit avoided crossing and level repulsion.
• Demonstrated similarity to energy level behavior in quantum chaos.
• Showed exponentially strong depletion in level spacing distributions at small values.

Conclusions:

• The behavior of Lyapunov exponents mirrors quantum chaos.
• Random matrix theory provides a framework for understanding these dynamics.
• Results offer insights into the statistical properties of chaotic systems.