Functional renormalization group approach – an alternative route to go beyond mode coupling theory

On the coarse-grained level of hydrodynamic fluctuations we briefly present a new approach for analyzing the complex transport behavior in dense compressible fluids. Starting from a generic class of nonlinear Langevin equations we derive a set of functional differential equations for the dimensionless transport coefficients. The functional structure of these flow equations represents the interplay between fast thermal fluctuations and the nonlinear coupling of the slow field variables. We obtain, that these equations do not show a critical physical fixed point. Our results provide an interesting tool to investigate the long-wavelength and low-frequency behavior in dense fluids in terms of a functional renormalization group formalism for not necessarily critical systems.