Symmetry breaking and restoration in the Ginzburg-Landau model of nematic liquid crystals

Thursday, March 1, 2018 - 3:30pm - 4:20pm
Lind 305
Michal Kowalczyk (University of Chile)
In this talk I will discuss qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals near the Friedrichs transition. This model depends on two parameters: ɛ>0 which is small and represents the coherence scale of the system and a≧ 0 which represents the intensity of the applied laser light. I will focus on the phenomenon of symmetry breaking as a and ɛ vary and I will show that when a=0 the global minimizer is radially symmetric and unique and that its symmetry is instantly broken as a>0 and then restored for sufficiently large values of a. Symmetry breaking is associated with the presence of a new type of topological defect which we named the shadow vortex. The symmetry breaking scenario is a rigorous confirmation of experimental and numerical results. I will also
describe similar results in the one and two dimensional scalar versions of the model. Finally I will show that the new topological defects are locally described by the second Painlevé equation.