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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 090, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.090
(Mi sigma118)
 

This article is cited in 9 scientific papers (total in 9 papers)

Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics

Peter A. Horváthy

Laboratoire de Mathématiques et de Physique Théorique, Université de Tours, Parc de Grandmont, F-37200 Tours, France
Full-text PDF (268 kB) Citations (9)
References:
Abstract: Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the “exotic” particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Keywords: non-commutative mechanics; semiclassical models; Hall effect.
Received: September 25, 2006; in final form November 27, 2006; Published online December 14, 2006
Bibliographic databases:
Document Type: Article
MSC: 81V70; 81T75
Language: English
Citation: Peter A. Horváthy, “Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics”, SIGMA, 2 (2006), 090, 9 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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