Hopping models of charge transfer in a complex environment: coupled memory continuous-time random walk approach

Area of Science:

• Complex media physics
• Charge transport phenomena
• Statistical mechanics

Background:

• Disordered complex media exhibit anomalous charge transport with slow relaxation.
• Broad distributions of relaxation times are typically used to describe these systems.
• Standard kinetic approaches include continuous-time random walks (CTRWs) and fractional diffusion.

Purpose of the Study:

• To demonstrate the power of the CTRW approach for modeling charge transport in complex media.
• To generalize the standard CTRW model to coupled memory CTRWs.
• To apply this generalized model to understand nonexponential electron-transfer processes.

Main Methods:

• Utilizing probabilistic formalism and limit theorems within the CTRW framework.
• Developing a new class of coupled memory CTRWs.
• Applying the generalized CTRW model to systems with dynamics-controlled electron transfer.

Main Results:

• Rigorous prediction of limiting distributions for charge paths.
• Derivation of effective relaxation properties for complex systems.
• Demonstration that coupled memory CTRWs can yield the Havriliak-Negami response.

Conclusions:

• The CTRW approach provides a powerful tool for analyzing anomalous charge transport.
• Coupled memory CTRWs offer a versatile framework for modeling complex relaxation phenomena.
• This method is applicable to understanding electron-transfer processes influenced by environmental dynamics.