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Subordination approach to Lyapunov exponents in random systems with memory
1Solid State Institute, Technion, Haifa 32000, Israel.
Chaos (Woodbury, N.Y.)
|November 3, 2025
Summary
We developed a subordination approach for non-Markovian random processes with power-law correlated noise. This method reveals exponential growth in eigenfunctions, relating to Anderson localization and determining wave function localization length.
Area of Science:
- Statistical Physics
- Quantum Mechanics
Background:
- Langevin equations are fundamental for modeling stochastic processes.
- Non-Markovian and non-Gaussian processes present significant analytical challenges.
- Anderson localization describes wave function decay in disordered potentials.
Purpose of the Study:
- To develop a subordination approach for Langevin equations with colored, power-law correlated noise.
- To analyze the behavior of eigenfunctions and their derivatives in such systems.
- To connect these findings to the phenomenon of Anderson localization.
Main Methods:
- Studied a Langevin equation with specific noise characteristics.
- Developed and applied a standard subordination approach.
- Analyzed the exponential growth of second moments and Lyapunov exponents.
Main Results:
- Derived the exponential growth of second moments for eigenfunctions and their derivatives.
- Established a connection between the noise properties and Anderson localization.
- Obtained values characterizing the asymptotic behavior of localized wave functions.
Conclusions:
- The developed subordination approach effectively handles non-Markovian and non-Gaussian processes.
- The study provides insights into Anderson localization in systems with memory.
- The results determine the localization length of wave functions in random potentials.
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