Non-equilibrium classical, quantum and active fluids

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Non-equilibrium systems come in a much larger variety than in equilibrium and their statistical description and classification remains a major task. The NEQfluids project aims to provide a unified view of systems that can be described as non-equilibrium fluids, using the framework of the functional non-perturbative renormalization group. These systems range from incompressible classical fluids, compressible classical and quantum fluids, to dark matter and active matter. NEQfluids will concentrate expertise and effort across traditional discipline boundaries to reach a better understanding from first principles of these non-equilibrium fluids. We will specifically address four challenges:Fully developed classical turbulence: the aim is to obtain a quantitative understanding of the statistical properties of classical turbulence for incompressible fluids described by the Navier-Stokes equations.Active matter: we want to understand common features at the collective scale of the collective motion of self-propelled living or artificial systems such as flocks of birds, bacteria colonies, or bio-polymers, focusing on two specific cases, polar-ordered flocks and active smectics.Fluid properties of quantum fields: we will compute ab initio the macroscopic properties of fluids for which a microscopic description as a relativistic (or non-relativistic) quantum field theory is known.Macroscopic properties of dark matter and cosmological large-scale structures: our goal is to develop a detailed renormalization group theory of cosmological structure formation.These different problems will be treated by a unified approach based on the functional renormalization group (fRG), which is a modern formulation of Wilson’s original ideas. The fRG is based on an exact flow equation, whose simple form permits approximations that are not based on a series expansion in a “small” parameter, but rather rely on a truncated functional space. This non-perturbative method has been shown to yield accurate results even when the theory is strongly coupled. It is versatile and can be used for classical and quantum systems, in or out of thermal equilibrium, for any field content and in any dimension. The main asset of the NEQfluids consortium is its expertise on these versions of this powerful theoretical tool.Close collaboration between the different tasks and partners is an essential aspect for the completion of this project. Interactions between partners will be facilitated by the many deep connections and parallels at a theoretical level between the systems studied. They are all non-equilibrium in nature, and described in a common theoretical framework (classical Martin-Siggia-Rose-Janssen-de Dominicis response field formalism, or quantum field theoretic Schwinger-Keldysh technique). Moreover, the systems share similar symmetries. Fruitful cross-fertilization between domains will help for substantial advances in the understanding of these different physics problems.