Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry breaking and restoration in the Ginzburg-Landau model of
  nematic liquid crystals   In this paper we study 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 is
depends on two parameters: $\epsilon>0$ which is small and represents the
coherence scale of the system and $a\geq 0$ which represents the intensity of
the applied laser light. In particular we are interested in the phenomenon of
symmetry breaking as $a$ and $\epsilon$ vary. We 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
obtained in our earlier work.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom