Novel Mathematical Approach for Random 3D Spin System Under the Influence of External Field. Generalization of Clausius-Mossotti Equation
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.
Ch. Kittel, Introduction to Solid State Physics, J. Wiley and sons, Inc., New York, London, Sydney, Toronto, 1962.
D.J. Griffith, Introduction to Electrodynamics, Prentic Hall, New Jersy, 192 (1989).
R. Becker, Electromagnetic Fields and Interactions, Dover, New York, 95 (1972).
Y. Tu, J. Tersoff and G. Grinstein, Phys. Rev. Lett., 81, 4899 (1998).
I.M. Lifshits, S.A. Gredeskul, L.A. Pastur, Introduction to the theory of disordered systems, Moscow, Nauka, (in Russian) 1982.
A.V. Bogdanov, A.S. Gevorkyan and A.G. Grigoryan, AMS/IP Studies in Adv. Mathematics, 13, 81 (1999).
A.S. Gevorkyan and Chin Kun Hu, Proceedings of the ISAAC Conf. on Analysis, Yerevan, Armenia, Eds. by G.A. Barsegian et.al., 164 (2004).
L. Berthier and A.P. Young, Time and length scales in spin glass, arXiv;condnat/0310721v130Oct2003.
P.V. Pavlov, A.F. Khokhlov, Solid State Physics, High School Book Company, Moscow, (in Russian) 2000.
G.A. Korn and T.M. Korn, Mathematical Handbook, for scientist and engineers, McGraw-Hill Book Company, New York, 1968.
W.H. Zachariasen, J. Am. Chem. Soc. 54, 3841 (1932).
K. Binder and A.P. Young, Rev. Mod. Physics, 58, 4, 801 (1986).
Ch. Dasgurta, Shang-keng Ma, and Chin-Kun Hu, Phys. Rev. B 20, 3837 (1979).
J.L. van Hemmen, In Proceedings of the Heidelberg Coloquium on Spin Glasses, ed. By J.L. van Hemmen and I. Morgenstern, Lecture Notes in Physics 192, (Spinger, Berlin, 1983).
B.A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
M. Abramowitz and I. Stegun, Handbook of mathematical functions, Nat. Bureau of standards Applied Mathematics Series-55, 1964.
S.F. Edwards and P.W. Anderson, J. Phys. F 9, 965 (1975).
M.V. Fedoryuk, Method of saddle-point, Moscow, Nauka, (in Russian) 1977.
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