Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface
| Autor: | Saberi, A. A., Niry, M. D., Fazeli, S. M., Tabar, M. R. Rahimi, Rouhani, S. |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 77, 051607 (2008) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.77.051607 |
| Popis: | The statistics of the iso-height lines in (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformal invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of new exact analytical results for the KPZ dynamics. We present direct evidence that the iso-height lines can be described by the family of conformal invariant curves called Schramm-Loewner evolution (or $SLE_\kappa$) with diffusivity $\kappa=8/3$. It is shown that the absence of the non-linear term in the KPZ equation will change the diffusivity $\kappa$ from 8/3 to 4, indicating that the iso-height lines of the Edwards-Wilkinson (EW) surface are also conformally invariant, and belong to the universality class of the domain walls in the O(2) spin model. Comment: 4 pages, 6 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|