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arXiv 2002.08323hep-th
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相对论性因果流体中的非线性涨落

Nonlinear Fluctuations in Relativistic Causal Fluids

Nahuel Mirón-Granese, Alejandra Kandus, Esteban Calzetta

备注：
41 pages, no figures. References updated. This arXiv file replaces former arXiv:1812.01003 because we addressed the studied problem with a more consistent and powerful formalism. In view of these major changes, the former arXiv file was withdrawn and replaced with the present manuscript. Published in JHEP
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摘要：

在真实相对论流体的二阶理论中，流体的非理想性质是用一组新的动力学张量变量来描述的。在这项工作中，我们将探讨这些变量在保形流体的非线性动力学。在所有可能的SOT中，我们选择使用发散型理论（DTT）形式主义，这确保了热力学第二定律的非微扰实现。张量模包括两个无发散模，这两个模在基于纳维-斯托克斯方程的协变推广的理论中没有类似物，并且这两个模特别相关，因为它们线性耦合到引力场。为了研究这个不可约的张量扇区的动力学，我们观察到在DTTs等因果理论中，热涨落会引起随机搅拌力，从而激发张量模式，同时保持能量动量守恒。从涨落耗散的考虑出发，可以得出随机力是高斯型的，具有白色谱。不可约的张量模式反过来激发矢量模式，后者对张量扇区产生反作用，从而产生一致的非线性，二阶描述的无发散张量动力学。利用Martin-Siggia-Rose（MSR）形式和两粒子不可约有效作用量（2 PIEA）形式，得到了该模型相关的两点关联函数：延迟传播子和Hadamard函数的单圈修正方程.不可约张量模式在这个顺序的自洽动力学的总体结果是在紫外部门的频谱耗尽，这表明张量模式可以维持一个逆熵级联。

英文摘要：

In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties of the flows are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those variables in a conformal fluid. Among all possible SOTs, we choose to work with the Divergence Type Theories (DTT) formalism, which ensures that the second law of thermodynamics is fulfilled non-perturbatively. The tensor modes include two divergence-free modes which have no analog in theories based on covariant generalizations of the Navier-Stokes equation, and that are particularly relevant because they couple linearly to a gravitational field. To study the dynamics of this irreducible tensor sector, we observe that in causal theories such as DTTs, thermal fluctuations induce a stochastic stirring force, which excites the tensor modes while preserving energy momentum conservation. From fluctuation-dissipation considerations it follows that the random force is Gaussian with a white spectrum. The irreducible tensor modes in turn excite vector modes, which back-react on the tensor sector, thus producing a consistent non-linear, second order description of the divergence-free tensor dynamics. Using the Martin-Siggia-Rose (MSR) formalism plus the Two-Particle Irreducible Effective Action (2PIEA) formalism, we obtain the one-loop corrected equations for the relevant two-point correlation functions of the model: the retarded propagator and the Hadamard function. The overall result of the self-consistent dynamics of the irreducible tensor modes at this order is a depletion of the spectrum in the UV sector, which suggests that tensor modes could sustain an inverse entropy cascade.

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