Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions
Abstract
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 tc. 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 tc and the singularity time scale tc, 0 of the KPZ equation with an infinitesimal surface tension is investigated.
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