Anomalous diffusion, localization, aging, and subaging effects in trap models at very low temperature.

Area of Science:

• Statistical Physics
• Condensed Matter Physics

Background:

• The dynamics of disordered systems are complex.
• Trap models describe systems with energy barriers.

Purpose of the Study:

• To analyze the one-dimensional symmetric trap model dynamics.
• To investigate aging and subaging effects.
• To generalize the model and explore its behavior in higher dimensions.

Main Methods:

• Exact real-space renormalization procedure at zero temperature.
• Series expansion in temperature (T) for corrections.
• Scaling analysis for two-dimensional systems.

Main Results:

• Explicit results for observables at T=0, including diffusion front and localization parameters.
• Reproduction of distinct aging exponents and scaling functions.
• Identification of alpha-independent large-scale effective models at low temperatures.
• Determination of two key time scales for aging in 2D.

Conclusions:

• The real-space renormalization group method provides exact results at T=0 and systematic corrections.
• The generalized trap model's low-temperature behavior is largely independent of the alpha parameter.
• The study clarifies aging dynamics and scaling properties in trap models.