Ballistic deposition with memory:a new universality class of surface growth with a new dynamical scaling

Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where memory of a deposition at a site induces more depositions at that site or its neighbors. By studying the statistics of surfaces in this model, we obtain three independent critical exponents: the growth exponent $\beta =5/4$, the roughening exponent $\alpha = 2$, and the new (size) exponent $\gamma = 3/4$. The model requires a modification to the Family-Vicsek scaling, resulting in the dynamical exponent $z = \frac{\alpha-\gamma}{\beta} = 1$. This modified scaling collapses the surface width vs time curves for various lattice sizes. This is a previously unobserved universality class of surface growth where the KPZ universality is an unstable fixed point of the dynamics.