Poincar\'e-like approach to Landau Theory. I. General theory
Mathematical Physics
2015-10-28 v1 Soft Condensed Matter
math.MP
Classical Physics
Abstract
We discuss a procedure to simplify the Landau potential, based on Michel's reduction to orbit space and Poincar\'e normalization procedure; and illustrate it by concrete examples. The method makes use, as in Poincar\'e theory, of a chain of near-identity coordinate transformations with homogeneous generating functions; using Michel's insight, one can work in orbit space. It is shown that it is possible to control the choice of generating functions so to obtain a (in many cases, substantial) simplification of the Landau polynomial, including a reduction of the parameters it depends on. Several examples are considered in detail.
Keywords
Cite
@article{arxiv.1510.05443,
title = {Poincar\'e-like approach to Landau Theory. I. General theory},
author = {G. Gaeta},
journal= {arXiv preprint arXiv:1510.05443},
year = {2015}
}