# Novel Mathematical Approach for Random 3D Spin System Under the Influence of External Field. Generalization of Clausius-Mossotti Equation

## Abstract

A dielectric medium consisting of roughly polarized molecules has been treated as a 3D disordered spin system. For investigation of statistical properties of this system on scales of space-time periods of standing electromagnetic wave a microscopic approach has been developed. Using the Birgoff ergodic hypothesis the initial 3D spin problem is reduced to two conditionally separate 1D problems along external electromagnetic field propagation. The first problem describes a quantum dynamics of disordered N-particles system with relaxation, while the second one describes statistical properties of steric disordered spin chain system. Based on developed in both problems constructions, the coefficient of polarizability related to collective orientational effects was calculated. The Clausius-Mossotti equation for dielectric constant was generalized on the micrometer space and nanosecond time scales.

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*Mathematical Problems of Computer Science*,

*29*, 36–50. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/446

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