Fluctuational Effects in the Dynamics of Liquid Crystals

1 Nematic Liquid Crystals.- 1.1 Thermodynamics of Nematics.- 1.2 The Poisson Brackets Method.- 1.3 Equations of Hydrodynamics for Nematics.- 1.4 Eigenmode Spectrum of Nematics.- 2 Smectic Liquid Crystals.- 2.1 Static Properties of Smectics.- 2.2 Equations of Hydrodynamics for Smectics.- 2.3 Linear Eigenmode Spectrum of Smectics.- 3 Fluctuation Effects in Smectic Liquid Crystals.- 3.1 Static Fluctuations.- 3.2 Diagram Technique for Dynamic Effects.- 3.3 Effective Action for Smectics.- 3.4 Renormalization of the Effective Action.- 3.5 Fluctuation Corrections to the Spectrum.- 4 Columnar Phases of Liquid Crystals.- 4.1 Static Properties of Columnar Phases.- 4.2 Hydrodynamic Equations for Columnar Phases.- 4.2 Linear Spectrum of Columnar Phases.- 4.4 Fluctuation Effects in Columnar Phases.- 5 Chiral Liquid Crystals.- 5.1 Peculiarities of Static Properties of Cholesterics.- 5.2 Macroscopic Dynamics of Cholesterics.- 5.3 Static Properties of Chiral Smectics.- 5.4 Dynamics of Chiral Smectics.- 5.5 Dynamics of Compensated Cholesterics.- 6 Freely Suspended Films.- 6.1 Static Properties of the Films.- 6.2 Dynamical Equations of the Films.- 6.3 Dynamical Fluctuational Effects of the Films.- 6.4 Spectrum of Eigenmodes of the Films.- 7 Langmuir Films and Membranes.- 7.1 Thermodynamics of Langmuir Films.- 7.2 Dynamic Equations of Langmuir Films.- 7.3 The Spectrum of Surface Modes.- 7.4 Membranes.- Conclusion.- References.

Liquid crystals are widely used in displays for electronic equipment and other applications. The authors provide a theoretical framework for understanding the nonlinear fluid dynamics of liquid crystals and the role played by thermal fluctuations. The techniques they use are of general use, and this exposition should thus be of interest to all condensed-matter theorists.