POISSON BRACKET METHOD AND ITS APPLICATIONS TO QUASICRYSTALS, LIQUID CRYSTALS AND A CLASS OF SOFT MATTER

This paper gives an introduction on the Poisson bracket method in condensed matter physics, Lie group and Lie algebra and their some applications to quasicrystals, liquid crystals and a class of soft matter. It introduces not only derivation on hydrodynamic or elasto-hydrodynamic equations of the materials, but also solutions of relevant equations, some among them explore the mistakes of well-known classic solutions, in addition, the equations and solutions on soft matter quasicrystals are observed for the first time.