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1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.
Physical Review Letters
|May 13, 2011
Summary
We introduce a novel stochastic process to study subdiffusion in disordered systems. This method offers an alternative to renormalization group techniques, applicable across all disorder strengths.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Stochastic Processes
Background:
- Subdiffusion is a key phenomenon in disordered systems.
- The quenched trap model describes anomalous diffusion.
- Renormalization group methods are commonly used but can be complex.
Purpose of the Study:
- To develop a new method for investigating subdiffusion.
- To analyze the quenched trap model using a novel stochastic process.
- To provide an alternative to existing renormalization group solutions.
Main Methods:
- Mapping the quenched trap model to a new stochastic process.
- Utilizing Brownian motion stopped at a specific operational time.
- Defining operational time based on site visitation numbers and disorder strength (α).
Main Results:
- The new stochastic process effectively models subdiffusion.
- In the zero-temperature limit, results match established renormalization group solutions.
- The approach is versatile, handling various strengths of disorder.
Conclusions:
- The proposed stochastic process is a powerful tool for studying subdiffusion.
- This method offers a viable alternative to renormalization group techniques.
- The framework is applicable to a wide range of disorder strengths in physical systems.
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