Seminário Geral: Geometry dependence in surface growth

Resumo: The kinetic roughening of evolving interfaces can occur in scales ranging from nanometers (e.g., in thin film deposition) to dozen of meters (e.g., in forest fire fronts), but in all cases one observes that the statistics of the height fluctuations display universal behaviors, allowing us to group them into a few universality classes. Among these, the Kardar-Parisi-Zhang (KPZ) class is the most important, once it encompasses also a diversity of other non-equilibrium systems, such as directed polymers in random media, particle transport and etc. A number of recent works on one-dimensional (1D) KPZ systems have demonstrated that their height distributions (HDs) and 2-point correlators are universal, but dependent on the geometry of the interface. Namely, the 1D KPZ class splits into two subclasses depending on whether the interfaces are flat or curved. The discovery of this geometry dependence (and subsequent development of this topic, including an exact solution of the 1D KPZ equation) is one of the main reasons why Prof. Herbert Spohn was awarded the Boltzmann Medal this year. In this talk, I will outline these advances on 1D KPZ systems, presenting our contributions in demonstrating their universality. Then, our efforts in generalizing the 1D KPZ scenario to 2D KPZ class, as well as to other universality classes will be discussed. In all cases, a splitting is observed in the HDs and correlators similarly to the ones in 1D KPZ systems, demonstrating that geometry dependence is a general feature of growing surfaces.