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Amoebas of Complex Hypersurfaces in Statistical Thermodynamics
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Mathematical physics, analysis and geometry, ISSN 1385-0172, E-ISSN 1572-9656, Vol. 16, no 1, 89-108 p.Article in journal (Refereed) Published
Abstract [en]

The amoeba of a complex hypersurface is its image under the logarithmic projection. A number of properties of algebraic hypersurface amoebas are carried over to the case of transcendental hypersurfaces. We demonstrate the potential that amoebas can bring into statistical physics by considering the problem of energy distribution in a quantum thermodynamic ensemble. The spectrum of the ensemble is assumed to be multidimensional; this leads us to the notions of multidimensional temperature and a vector of differential thermodynamic forms. Strictly speaking, in the paper we develop the multidimensional Darwin-Fowler method and give the description of the domain of admissible average values of energy for which the thermodynamic limit exists.

Place, publisher, year, edition, pages
2013. Vol. 16, no 1, 89-108 p.
Keyword [en]
Amoeba of complex hypersurface, Asymptotics of Laurent coefficients, Logarithmic Gauss mapping, Darwin-Fowler method
National Category
URN: urn:nbn:se:su:diva-88988DOI: 10.1007/s11040-012-9122-xISI: 000316020400004OAI: diva2:615447


Available from: 2013-04-10 Created: 2013-04-08 Last updated: 2013-04-10Bibliographically approved

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ReferencesLink to record
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