On the Theory of Relaxation for Systems with “Remnant” Memory

The investigation of the universal response of an electromagnetic, acoustic, and mechanical force indicates the existence of relaxation processes with memory. It is shown that the form of the polarization current I(t) ∼ (ω p t ) −(1+ m ) for (ω p t ≫ 1) can be explained on the basis of a dipole relaxation with a “remnant” memory. In accordance with theexperimental data a memory function is found which describes in one case the exponential decay I(t) ∼ exp (—λ t ) which is equivalent to the absence of memory and in the another case it transforms into a harmonic oscillator equation (full memory). From this theory theexistence of a “superslow” relaxation process also follows, in which the changing of polarization is slower than its first derivative. Such processes are also observed experimentally and are described by linear differential equations in fractional derivatives. The relationship between the experimental exponent m and the derivative exponent λ is found.