Diffusion with a broad class of stochastic diffusion coefficients.

Area of Science:

• Physics
• Physical Chemistry
• Biophysics

Background:

• Brownian motion is a fundamental model for diffusion.
• Stochastic diffusion coefficients (DCs) introduce complexity beyond standard models.
• Understanding anomalous diffusion is crucial in various scientific fields.

Purpose of the Study:

• Investigate diffusion properties with a broad class of stochastic diffusion coefficients.
• Characterize the propagator's behavior in finite and long time limits.
• Compare diffusion with stochastic DCs to deterministic DCs and fractional Brownian motion.

Main Methods:

• Analysis of diffusion processes with stochastic DCs, distinct from subordination approaches.
• Mathematical derivation and characterization of the particle propagator.
• Examination of ergodicity and its impact on propagator convergence.

Main Results:

• The propagator exhibits non-Gaussian and heavy-tailed characteristics for finite diffusion times.
• Particles with stochastic DCs can diffuse farther than those with deterministic DCs or fractional Brownian motion over finite times.
• For ergodic stochastic DCs, the propagator converges to a Gaussian distribution in the long time limit.

Conclusions:

• Stochastic diffusion coefficients lead to significant deviations from standard diffusion models at finite times.
• The long-time behavior of diffusion with stochastic DCs is predictable and Gaussian, with convergence rate influenced by the DC's autocovariance.
• This study provides new insights into anomalous diffusion phenomena.