Non-local meta-conformal invariance in diffusion-limited erosion

Abstract

The non-stationary relaxation and physical ageing in the diffusion-limited erosion process ({\sc dle}) is studied through the exact solution of its Langevin equation, in $d$ spatial dimensions. The dynamical exponent $z=1$, the growth exponent $\beta =\max (0,(1-d)/2)$ and the ageing exponents $a=b=d-1$ and ${\lambda }_C={\lambda }_R=d$ are found. In $d=1$ spatial dimension, a new representation of the meta-conformal Lie algebra, isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$, acts as a dynamical symmetry of the noise-averaged {\sc dle} Langevin equation. Its infinitesimal generators are non-local in space. The exact form of the full time-space dependence of the two-time response function of {\sc dle} is reproduced for $d=1$ from this symmetry. The relationship to the terrace-step-kink model of vicinal surfaces is discussed.

11 pages, no figures, final form

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Cited by in corpus (4)

• Schrödinger symmetry: a historical review
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Fractional diffusion equations interpolate between damping and waves
• Meta-conformal algebras in $d$ spatial dimensions