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Anomalous diffusion of particles driven by correlated noise
1Department of Mechanics and Mathematics, Sumy State University, 2, Rimskiy-Korsakov Street, 40007 Sumy, Ukraine.
Summary
We analyzed how random forces affect damped particle motion, deriving exact formulas for particle dispersion. Our findings reveal conditions for anomalous diffusion, linking it to noise correlations.
Area of Science:
- Statistical physics
- Nonlinear dynamics
- Complex systems
Background:
- Understanding particle dynamics under external forces is crucial in various scientific fields.
- Damped systems are common in physics and engineering, often influenced by random fluctuations.
- Anomalous diffusion deviates from standard Brownian motion, requiring specialized theoretical frameworks.
Purpose of the Study:
- To investigate the impact of arbitrary stationary random forces on damped particle motion.
- To derive exact analytical expressions for particle position and velocity dispersion.
- To explore the relationship between anomalous diffusion and the characteristics of noise correlations.
Main Methods:
- Utilized the Langevin equation framework to model particle dynamics.
- Derived exact expressions for statistical moments (dispersion) of particle position and velocity.
- Analyzed the conditions leading to anomalous diffusion by examining noise correlation functions.
Main Results:
- Obtained exact formulas for the dispersion of particle position, velocity, and their cross-dispersion.
- Identified specific noise correlation properties that induce anomalous diffusion.
- Demonstrated anomalous diffusion in both overdamped and undamped particle systems.
Conclusions:
- The study provides a comprehensive theoretical framework for understanding damped particle motion under random forces.
- Established a direct link between noise correlation functions and the emergence of anomalous diffusion.
- The derived expressions and analysis offer valuable insights for systems exhibiting complex dynamics.
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