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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster: Nonlinear Dynamics, Pattern Formation, Granular Matter

DY 27.1: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P4

Statistical field theory of linear spatio-temporally extended systems with multiplicative noise — •Frederik Gareis, David Aderbauer, and Michael Wilczek — Theoretische Physik I, Universität Bayreuth, Universitätsstr. 30, 95447 Bayreuth

Linear systems with multiplicative stochastic noise commonly exhibit non-Gaussian behavior in both space and time. We consider a classic example from statistical hydrodynamics, the Kraichnan model for a passive scalar convected in a stochastic velocity field. Describing such systems via a characteristic functional elegantly encodes the full statistics of the fields. However, the analysis of the resulting functional differential equations remains challenging due to the mathematical intricacy of treating second-order functional derivatives. Here, we show that a broad variety of such problems permit a solution of the functional differential equations in the form of a superposition of Gaussian functionals, even if the noise is correlated in space and time. While the linear terms, excluding the multiplicative noise, are compatible with Gaussian solutions, averaging over the multiplicative advection term introduces non-Gaussian statistics. Our approach provides a starting point for various systematic approximations such as a perturbation theory in terms of small multiplicative noise strength. On a conceptual level, it allows us to gain insights into the emergence of non-Gaussianity and intermittency, which could be relevant beyond statistical hydrodynamics.

Keywords: Statistical hydrodynamics; Intermittency; Characteristic functional; Stochastic PDEs; Gaussian decomposition