Anomalous relaxation and dielectric response.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• Dielectric response functions of glassy media are experimentally observed but lack a unified theoretical derivation.
• Existing phenomenological models (e.g., Cole-Cole, Davidson-Cole) describe these functions but lack a rigorous foundation.

Purpose of the Study:

• To derive known experimental dielectric response functions of glassy media from a fundamental theoretical framework.
• To establish a stochastic, thermodynamically consistent approach for understanding dielectric behavior in glasses.

Main Methods:

• Utilizing a generalized Langevin description for overdamped torsional dipole oscillators in random trapping potentials.
• Applying minimal assumptions to develop a non-Markovian theory that adheres to fundamental theorems.

Main Results:

• All known experimental (quasi)stationary dielectric response functions for glassy media were successfully derived.
• The developed non-Markovian theory satisfies the fluctuation-dissipation and Onsager regression theorems.
• The theory demonstrates no aging on the dielectric response timescale, assuming local thermal equilibrium.

Conclusions:

• The generalized Langevin description provides a firm theoretical basis for phenomenological dielectric models of glasses.
• Aging in glassy media occurs on timescales distinct from the primary dielectric response, potentially due to trap dynamics.
• This work offers a unified, stochastic, and thermodynamically consistent approach to dielectric phenomena in glassy systems.