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arXiv:1212.6156 · Journal of Physics A Mathematical and Theoretical

Non-local representations of the ageing algebra in higher dimensions

Stoimen Stoimenov, Malte Henkel

Published Jun 3, 2013• 11 citations
arXivHTMLPDF

Abstract

The ageing Lie algebra and especially its local representations for a dynamical exponent z = 2 have played an important role in the description of systems undergoing simple ageing, after a quench from a disordered state to the low-temperature phase. Here, the construction of representations of for generic values of z is described for any space dimension d > 1, generalizing upon earlier results for d = 1. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher order differential operators or the Riesz fractional derivative. Co-variant two-time response functions are derived. Some simple applications to the exactly solvable models of phase separation or interface growth with conserved dynamics are discussed.

DOI
10.1088/1751-8113/46/24/245004

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The ageing Lie algebra and especially its local representations for a dynamical exponent z = 2 have played an important role in the description of systems undergoing simple ageing, after a quench from a disordered state to the low-temperature phase. Here, the construction of representations of for generic values of z is described for any space dimension d > 1, generalizing upon earlier results for d = 1. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher order differential operators or the Riesz fractional derivative. Co-variant two-time response functions are derived. Some simple applications to the exactly solvable models of phase separation or interface growth with conserved dynamics are discussed.
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