Microscopic models for dielectric relaxation in disordered systems

Y.P. Kalmykov, Derrick Crothers, W.T. Coffey, S.V. Titov

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.
Original languageEnglish
Article number041103
Pages (from-to)041103
Number of pages1
JournalPhysical Review E
Issue number4 1
Publication statusPublished - Oct 2004

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics


Dive into the research topics of 'Microscopic models for dielectric relaxation in disordered systems'. Together they form a unique fingerprint.

Cite this