Non-equilibrium classical, quantum and active fluids

非平衡系统的种类比平衡系统多得多，它们的统计描述和分类仍然是一项主要任务。NEQ流体项目旨在利用功能非微扰重整化小组的框架，提供可被描述为非平衡流体的系统的统一视图。这些系统的范围从不可压缩的经典流体、可压缩的经典流体和量子流体，到暗物质和活性物质。NEQ流体将集中专业知识和努力，跨越传统学科界限，从这些非平衡流体的基本原理中更好地理解它们。我们将具体解决四个挑战：完全发展的经典湍流：目的是定量地了解由Navier-Stokes方程描述的不可压缩流体的经典湍流的统计特性。活动物质：我们想要了解自行式生物或人工系统(如鸟群、细菌群体或生物聚合物)集体运动的集体尺度上的共同特征，重点放在两个特定的情况下。量子场的流体性质。量子场的流体性质：我们将从头计算流体的宏观性质，微观描述为相对论(或非相对论)量子场论。暗物质和宇宙学大尺度结构的宏观性质：我们的目标是发展一个详细的宇宙结构形成的重整化群理论。这些不同的问题将通过基于泛函重整化群(FRG)的统一方法来处理，FRG是威尔逊原始思想的现代表述。FRG基于精确的流动方程，其简单的形式允许不基于“小”参数的级数展开的近似，而是依赖于截断的函数空间。这种非摄动方法已被证明即使在理论强耦合的情况下也能产生准确的结果。它是通用的，可以用于经典和量子系统，在热平衡或不热平衡，任何领域的内容和任何维度。NEQ流体联盟的主要资产是其在这些版本的强大理论工具方面的专业知识。不同任务和合作伙伴之间的密切合作是完成此项目的一个重要方面。合作伙伴之间的互动将通过所研究的系统之间在理论层面上的许多深层次联系和相似之处而得到促进。它们本质上都是非平衡的，并在一个共同的理论框架中描述(经典的Martin-Siggia-Rose-Janssen-de Dominicis响应场形式主义，或量子场论的Schwinger-Keldysh技术)。此外，这两个系统具有相似的对称性。领域间卓有成效的相互促进将有助于在理解这些不同的物理问题方面取得实质性进展。

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.