Trace of anomalous diffusion in a biased quenched trap model

Area of Science:

• Statistical Physics
• Complex Systems Analysis

Background:

• Understanding diffusion in heterogeneous environments is crucial for various scientific fields.
• Quenched disorder introduces complexities not present in simpler models.

Purpose of the Study:

• To analytically investigate diffusion in quenched heterogeneous environments with bias.
• To explore first-passage-time statistics for drift and diffusion coefficient determination.
• To identify conditions leading to non-self-averaging behavior.

Main Methods:

• Analytical treatment of diffusion processes.
• Application of first-passage-time statistics.
• Analysis of periodic quenched environments.

Main Results:

• Identified transition points exhibiting large sample-to-sample fluctuations (non-self-averaging).
• Disorder average of diffusion coefficient diverges or becomes zero for superdiffusion or subdiffusion, respectively.
• Established a link between anomalous diffusion in annealed models and quenched model diffusion coefficients.

Conclusions:

• Non-self-averaging phenomena are significant in quenched heterogeneous systems.
• The behavior of diffusion coefficients in quenched models serves as an indicator for anomalous diffusion in annealed counterparts.