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Langevin dynamics of correlated subdiffusion and normal diffusion.

Yingxi Wang¹, Nanrong Zhao, YiJing Yan

¹College of Chemistry, Sichuan University, Chengdu 610064, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 12, 2012

Summary

This study examines particle dynamics using a generalized Langevin equation. Couplings affect long-time behavior, extending time scales for free particles and retarding relaxation for bounded particles.

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Area of Science:

Statistical Mechanics
Non-equilibrium Physics
Complex Systems

Background:

Generalized Langevin Equation (GLE) describes complex dynamics.
Fractional Gaussian noise (fGn) and white noise introduce memory and stochasticity.
Coupled noise models are crucial for realistic systems.

Purpose of the Study:

Analyze dissipative particle dynamics under coupled fractional Gaussian and white noise.
Investigate the influence of fluctuation correlation and interoscillator coupling.
Examine behavior in free and harmonic potential systems.

Main Methods:

Derivation of general expressions for mean values, variances, and velocity autocorrelation function.
Numerical Laplace inversion technique for temporal evolution analysis.
Analytical investigation of short-time and long-time behaviors.

Main Results:

Couplings do not impact short-time self-diffusion, which mirrors 1D systems.
Fluctuation correlation extends time scales for free particle self-diffusion.
Interoscillator coupling retards relaxation for bounded particles; cross-diffusion emerges.

Conclusions:

Coupling effects are prominent in long-time dynamics, distinguishing free and bounded particle behaviors.
The interplay of noise types and coupling dictates particle diffusion characteristics.
Cross-diffusion emergence highlights complex emergent behaviors in multi-dimensional systems.