Dynamics of uniaxial nematic liquid crystals with rod-shaped and disc-shaped molecules in an external field is considered. For the systems under study thermodynamics is constructed and nonlinear dynamic equations accounting for the internal spatial anisotropy and molecules shape are derived. Densities of additive integrals of motion and corresponding flow densities are introduced in terms of thermodynamic potential. Analytical structure of low-frequency asymptotics of two-time Green’s functions is calculated and their characteristics in the region of small wave vectors and frequencies are studied. It is shown that unlike other condensed media with spontaneously broken symmetry low-frequency asymptotics of Green’s functions of considered liquid crystals do not contain divergences of Bogolyubov type.
Martin, P.C., Parodi, O. and Pershan, P.J. (1972)
Unified hydrodynamic theory for crystals, liquid crystals and normal fluids Phys. Rev. A., 6, 2401-20.
Isayev, A., Kovalevsky, M. and Peletminsky, S. (1994) On
construction of Poisson brackets and dynamics of liquid crystals Mod. Phys. Lett. B., 8, 677-686.
Isaev, A.A.,
Kovalevsky, M.Y. and Peletminsky, S.V. (1996) Hamiltonian approach to the
theory of condensed media with spontaneously broken symmetry JINR, 27, 431-492 (in Russian).
Ivashin, A.P., Kovalevsky, M.Y. and
Logvinova, L.V. (2004) Dynamics of nematic liquid crystals with conformational
degrees of freedom J. Quant. Chem., 100,
636-644.
Kovalevsky, M.Y.,
Logvinova, L.V. and Matskevych, V.T. (2009) Investigation of the influence of
molecule deformation on the dynamics and collective excitation spectra in
nematic liquid crystals JINR, 40,
704-753.
Malanoski, A.P., Greanya, V.A.,
Weslowski, B.T., Spector, M.S., Selinger, J.V. and Shashidhar, R. (2004) Theory
of the acoustic realignment of nematic liquid crystals Phys. Rev. E., 69, 021705-1-8.
Greanya, V.A., Malanoski, A.P.,
Weslowski, B.T., Spector, M.S. and Selinger, J.V. (2005) Dynamics of the
acousto-optic effect in a nematic liquid crystal Liq. Cryst., 32, 933-941.
Holovko, M.F., Sokolovska, T.G. (1999) Analytical
solution of the Ornstein-Zernike equation with the mean spherical closure for a
nematic phase J. Mol. Liq., 82, 161-181.
