KARDAR-PARISI-ZHANG MODEL AND ANOMALOUS ELASTICITY OF 2-DIMENSIONAL AND 3-DIMENSIONAL SMECTIC-A LIQUID-CRYSTALS

We reveal a deep theoretical relationship between equilibrium statisti cal physics of smectic-A liquid crystals and nonequilibrium statistica l physics of the Kardar-Parisi-Zhang dynamical model [M. Kardar, G. Pa risi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986)] for interfaces growing in the presence of a flux of incoming particles. This relatio nship provides an exact approach to study Landau-Peierls phenomena and anomalous elasticity of two-dimensional smectic- A liquid crystals. A lso, it yields prediction of an unusual elastic critical point in-thre e-dimensional smectic-A liquid crystals with broken inversion symmetry (head-to-tail packing of layers). We discuss the elasticity and fluct uations of these unusual smectic-A phases.