SYMMETRICAL AND TOPOLOGICAL ANALYSIS OF THE ORDER PARAMETER FLUCTUATIONS IN A NEMATIC LIQUID-CRYSTAL

The analysis of the order parameter fluctuations in nematic liquid cry stals is performed within the topological and symmetrical representati ons. It is shown that in SD space of the nematic order parameter repre sented by symmetric traceless second rank matrices there can occur onl y two cases corresponding to two types of orbits in 5D space. One case , the orbit being sphere S2, is characterized by two gapless and three gap modes of order parameter fluctuations. In the limit q --> 0 (q is the wavevector) two of gap modes are degenerate. The second case, SO( 3) being an orbit, is characterized by three gapless and two gap fluct uation modes degenerate in the limit q --> 0. Both the cases are reali zed experimentally and correspond to uniaxial and two-axial nematic li quid crystals. In uniaxial nematics a definite connection between vari ation of the order parameter components results from the condition of axial symmetry, corresponding to the degenerated gap and gapless modes . The dynamic aspects of symmetry and physical consequences of the wor k are discussed in brief.