2010/03/20 by Zon, Boris A.
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other)
paper · doi:10.48550/arxiv.1003.3917
We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence σ~ ωn where n<1 corresponds to empirical Jonscher's universal relaxation law while n>1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory.