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 Poincaré 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.
Poincaré-like approach to Landau theory. I: General theory / G. Gaeta. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 56:8(2015), pp. 083504.1-083504.25. [10.1063/1.4927425]
Poincaré-like approach to Landau theory. I: General theory
G. Gaeta
2015
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 Poincaré 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.File | Dimensione | Formato | |
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