1212.6156 (Stoimen Stoimenov et al.)

Non-local representations of the ageing algebra in higher dimensions    [PDF]

Stoimen Stoimenov, Malte Henkel

The ageing Lie algebra \mathfrak{age}(d) and especially its local representations for a dynamical exponent z=2 has played an important r\^ole 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 \mathfrak{age}(d) for generic values of z is described for any space dimension d>1, generalising 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 exactly solvable models of phase separation or interface growth with conserved dynamics are discussed.

View original: http://arxiv.org/abs/1212.6156