Non-equilibrium classical, quantum and active fluids – NEQfluids

The variety of non-equilibrium systems is much larger than in equilibrium and yet, their statistical description remains a major task. The NEQfluids project aims for a unified view by the use of functional renormalization of non-equilibrium systems which can be described as fluids, at least at a mesoscopic scale. They range from incompressible classical fluids, compressible classical and quantum fluids, to dark matter and active matter. The aim of NEQfluids is to concentrate expertise and effort across traditional borders between fields (and nations) towards a better understanding from first principles of these non-equilibrium fluids. We 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 Navier-Stokes equation.

Collective behavior of active matter: we want to understand common features of the macroscopic collective motion of self-propelled living or artificial systems such as flocks of birds, bacteria colonies, or bio-polymers, focusing on two specific systems, polar-ordered flocks and active smectic.

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 structure: our goal is to determine the macroscopic properties of different dark matter models and how they affect the cosmological large-scale structure formation.

Although these systems are clearly different, they will be tackled with a unified approach, based on functional renormalization group (fRG), which is a modern formulation of Wilson’s original ideas. It is based on an exact flow equation, whose simple form permits approximations that are not based on a series expansion in a “small” parameter. An approximate solution of the fundamental fRG equation relies on a truncated functional space. This non-perturbative method has demonstrated to yield accurate results even when the theory is strongly coupled. It is versatile and can be used for classical and quantum systems, at or out of thermal equilibrium, for any field content and in any dimension. The asset of NEQfluids is the common expertise of the partners on these powerful theoretical tools.

The close collaboration between the different tasks is an essential aspect for the completion of this project, to share progress and experience gained in each part. The interaction between the partners will be facilitated by 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. Besides the standard symmetries of the equations of motion (invariance under translation, rotation, Galilean or Lorentzian boost), they possess extended symmetries which play a crucial role in our theoretical approach, both on a conceptual level and technically for devising truncations. Fruitful cross-fertilization between domains will help for substantial advances in the understanding of these different physics problems.