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The Kardar-Parisi-Zhang (KPZ) equation provides one of the simplest non trivial examples of a Non-Equilibrium Steady State. Its universal features capture a very wide range of physical phenomena ranging from varied types of interfaces to turbulent hydrodynamic flows or thermodynamics of polymers in noisy environments. Enormous progress has been made in the last 10 years thanks to an exact derivation of the statistics of the KPZ dynamics in the case of one-dimensional systems driven by a stochastic white noise. The cases of higher dimensions and/or correlated noise remain however unsolved. In this presentation I discuss the physics of a one-dimensional interface that is subjected to a noise with smooth spatio-temporal correlations. This problem was previously studied numerically as well as with the Replica Trick in a Gaussian variational approach.It was found that the small scale features depend on the details of the microscopic noise while (up to the overall amplitude factors) the exact solution with white noise governs the large scales. In the present work, Functional Renormalisation Group (FRG) methods are employed in order to resolve the non-perturbative features of KPZ dynamics. The FRG makes it possible to follow the renormalisation group flow from its initial conditions all the way down to its fixed point, that is from microscopic dynamics to the large distance properties. I show that the exact solution emerges on large scales independently of the details of the noise correlations. Moreover the small scale features (and their dependence on the particular choice of the noise correlations) are resolved and compared to direct numerical simulations.

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Steven Mathey, University of Grenoble
Seminar room of the Institute of Physics II
Contact: Sebastian Diehl