Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Articles dans des revues à comité de lecture

Non-local meta-conformal invariance in diffusion-limited erosion
Henkel M.
J. Phys. A Math. Theor. 49 (2016) 49LT02
DOI : 10.1088/1751-8113/49/49/49LT02
ArXiv : arxiv:1606.06207 [PDF]

The non-stationary relaxation and physical ageing in the diffusion-limited erosion process (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 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 DLE is reproduced for $d=1$ from this symmetry. The relationship to the terrace-step-kink model of vicinal surfaces is discussed.



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