Universal Fluctuations of Single-Particle Diffusivity in a Quenched Environment

Area of Science:

• Physics
• Biophysics
• Materials Science

Background:

• Local diffusion coefficients in disordered materials, such as living cells, exhibit significant heterogeneity.
• Understanding single-particle diffusivity is crucial for various biological and material science applications.

Purpose of the Study:

• To investigate the effects of quenched disorder, sample disorder fluctuations, and confinement on single-particle diffusivity in finite systems.
• To analyze the non-self-averaging nature of diffusion in disordered systems.

Main Methods:

• Consideration of finite systems with quenched disorder.
• Analysis of time-averaged mean square displacement (MSD) for single particles.
• Investigation of disorder averaging and its dependence on system size.

Main Results:

• The system is ergodic for a single disorder realization but non-self-averaging, with MSD depending crucially on the disorder.
• The disorder average of the time-averaged MSD decreases as system size increases.
• A universal distribution for diffusivity is found, independent of system dimension.
• Fluctuations in single-particle diffusivity significantly exceed predictions from annealed theory, with notable confinement effects.

Conclusions:

• Disorder fluctuations and confinement play critical roles in single-particle diffusivity in heterogeneous systems.
• The non-self-averaging nature of diffusion must be considered for accurate modeling, especially in finite systems.
• Findings have implications for interpreting experimental data in biological and material science contexts.