Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain
1
Rechnergestützte Physik der Werkstoffe, Institut für Baustoffe (IfB), ETH Zürich, Stefano-Franscini-Platz 3, CH-8093 Zürich, Switzerland
2
Groupe de Physique Statistique, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandœuvre-lès-Nancy Cedex, France
Academic Editor: Roman M. Cherniha
Symmetry 2017, 9(1), 2; https://doi.org/10.3390/sym9010002
Received: 16 October 2016 / Revised: 18 November 2016 / Accepted: 14 December 2016 / Published: 24 December 2016
(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models)
Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent , none of the known variants of conformal invariance can act as its dynamical symmetry. In spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.
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Keywords:
meta-conformal invariance; representations; loop-Virasoro algebra; physical ageing; diffusion-limited erosion; terrace-step-kink model
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MDPI and ACS Style
Henkel, M. Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain. Symmetry 2017, 9, 2. https://doi.org/10.3390/sym9010002
AMA Style
Henkel M. Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain. Symmetry. 2017; 9(1):2. https://doi.org/10.3390/sym9010002
Chicago/Turabian StyleHenkel, Malte. 2017. "Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain" Symmetry 9, no. 1: 2. https://doi.org/10.3390/sym9010002
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