# 30th Marian Smoluchowski Symposium on Statistical Physics

3-8 September 2017
Poland timezone

## Exact solution for a $1+1$ etching model.

6 Sep 2017, 11:30
30m
oral

### Description

We present a method to derive analytically the growths exponents of a eroded surface whose dynamics is ruled by cellular automata. Starting from the automata, we write down the time evolution for the height's average and height's variance (roughness). We apply the method to the etching model[1,2] of $1+1$ dimensions, than we obtain the dynamical exponents, which perfectly match the numerical results obtained from simulations. Those exponents are exact and they are the same as those exhibited by the KPZ model[3] for this dimension. Therefore, it shows that the etching model and KPZ belong to the same universality class[4]. Moreover, we proof that in the continuous limit the majors terms leads to KPZ [5].  [1] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. Rev. E 63, 041113 (2001). [2] E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. Phys. A 48, 035001 (2015). [3] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56, 9, 889 (1986). [4] W. S. Alves, E. A. Rodrigues, H. A. Fernandes, B. A. Mello, F. A. Oliveira and I. V. L. Costa, Phys. Rev. E 94, 042119 (2016). [5] W. P. Gomes and F. A. Oliveira, to be published.