Non-local representations of the ageing algebra in higher dimensions

Abstract

The ageing Lie algebra age(d) and especially its local representations for a dynamical exponent z=2 has played an important rôle 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 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.

21 pages, LATEX2e (final form)

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Cited by in corpus (7)

• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Dynamical symmetries and causality in non-equilibrium phase transitions
• From dynamical scaling to local scale-invariance: a tutorial
• Physical ageing and new representations of some Lie algebras of local scale-invariance
• Fractional diffusion equations interpolate between damping and waves
• Fractional Galilean Symmetries
• On non-local representations of the ageing algebra in $d\ge 1$ dimensions