Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T15:46:56.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Closed and Exact Functions in the Context of Ginzburg–Landau Models

Published online by Cambridge University Press:  20 November 2018

Anamaria Savu
Anamaria Savu*
Affiliation:
Department of Mathematics, University of Northern British Columbia, Prince George, BC, V2N 4Z9 e-mail:, savua@unbc.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a general vector field we exhibit two Hilbert spaces, namely the space of so called closed functions and the space of exact functions and we calculate the codimension of the space of exact functions inside the larger space of closed functions. In particular we provide a new approach for the known cases: the Glauber field and the second-order Ginzburg–Landau field and for the case of the fourth-order Ginzburg–Landau field.

Keywords

42B0581Q5042A16Hermite polynomialsFock spaceFourier coefficientsFourier transformgroup of symmetries
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 3 , 01 June 2008 , pp. 685 - 702
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Kipnis, C. and Landim, C., Scaling Limits of Interacting Particle Systems. Grundlehren der MathematischenWissenschaften 320, Springer-Verlag, Berlin, 1999.Google Scholar
[2] Hatcher, A., Algebraic Topology. Cambridge University Press, Cambridge, 2002.Google Scholar
[3] Nagahata, Y., Fluctuation dissipation equation for lattice gas with energy. J. Statist. Phys. 110(2003), no.1-2, 219–246.Google Scholar
[4] Quastel, J., Diffusion of color in the simple exclusion process. Comm. Pure Appl. Math. 45(1992), no. 6, 623–679.Google Scholar
[5] Rudin, W., Fourier Analysis on Groups. Interscience Tracts in Pure and Applied Mathematics 12, Interscience Publishers, New York, 1962.Google Scholar
[6] Savu, A., Hydrodynamic scaling limit of continuum solid-on-solid model. J. Appl. Math. 2006 Article ID 69101, 37 pages.Google Scholar
[7] Varadhan, S. R. S., Nonlinear diffusion limit for a system with nearest neighbor interactions. II. In: Asymptotic Problems in Probability Theory: Stochastic Models and Diffusion on Fractals. Pitman Research Notes in Mathematics 283, Longman Sci. Tech., Harlow, 1993, pp. 75–128.Google Scholar
[8] Varadhan, S. R. S. and Yau, H. T., Diffusive limit of lattice gas with mixing conditions. Asian J. Math. 1(1997), no. 4, 623–678.Google Scholar