# Zero tension Kardar-Parisi-Zhang equation in d 1- Dimensions

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The joint probability distribution function PDF of the height and its gradients is derived for a zero tension $d+1$-dimensional Kardar-Parisi-Zhang KPZ equation. It is proved that the height`s PDF of zero tension KPZ equation shows lack of positivity after a finite time $t {c}$. The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale $t {c}$ and the singularity time scale $t {c, u \to 0}$ of the KPZ equation with an infinitesimal surface tension is investigated.

Autor: A. Bahraminasab; S. M. A. Tabei; A. A. Masoudi; F. Shahbazi; M. Reza Rahimi Tabar

Fuente: https://archive.org/