Corresponding Member H. H. Muminov From 2006 to present Doctor of Physical and Mathematical Sciences, Professor, Corresponding Member of the Academy of Sciences of Tajikistan Hikmat Halimovich Muminov is a Director of the Institute. He is renowned expert in the field of nonlinear mathematical physics and condensed matter theory. He developed the mathematical apparatus of generalized coherent states for higher spin values, which yields an adequate semiclassical description of quantum spin systems taking into account the excitation of multipole fields, on this basis the number of nonlinear evolution equations that describe magnetization dynamics, taking into account the multipole fields in ferro-and antiferromagnets with values spins 1 and 3 / 2, which cannot be reduced to the well-known Landau-Lifshitz equation. He developed a theory of geometric Berry phase for higher values of spin, on this basis a theory of tunneling in magnetic nano-molecules has been elaborated. Obtained and investigated new dynamical and topological solutions (in one- and two- spatial dimensions) of vector nonlinear sigma models of field theory.
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