Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport...

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Diffusion is a fundamental transport phenomenon linking microscopic molecular dynamics to macroscopic behavior.
• Understanding variations in diffusion coefficients, especially in biological systems, requires deeper theoretical insight.
• Current models may not fully capture the complexities of diffusion in dynamic environments.

Purpose of the Study:

• To investigate the transition from normal to anomalous diffusion using quantum scattering.
• To identify a physical attribute that explains variations in normal diffusion coefficients.
• To provide a theoretical framework for diffusion in complex biological systems.

Main Methods:

• Application of quantum scattering theory within the Boltzmann transport framework.
• Introduction of mean square displacement curvature as an order parameter.
• Utilization of quantum scattering length as a tuning variable (η).

Main Results:

• The curvature of mean square displacement effectively distinguishes normal, super-, and subdiffusion regimes.
• The critical point (η = ηc) of scattering length unambiguously determines the normal diffusion coefficient.
• A general expression for the effective linear collision operator was derived from quantum scattering amplitude.

Conclusions:

• Scattering length is a crucial dynamical characteristic for understanding diffusion in complex systems.
• The theoretical framework accurately rationalizes experimental observations in biological diffusion processes.
• A temperature-dependent effective voltage is proposed as a driver for molecular motion in diffusion.