Non-local representations of the ageing algebra in higher dimensions

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.