We develop further a kinetic theory of strings and derive a transport equation for a network of cosmic strings with Nambu-Goto evolution, interactions and background gravitational effects taken into account. We prove an H-theorem and obtain necessary and sufficient conditions for a thermodynamic equilibrium. At the lowest order the equilibrium is estimated by the von Mises-Fisher distributions parametrized by mean directions and dispersions of the right- and left-moving tangent vectors. Under assumption of a local equilibrium we derive a complete set of hydrodynamic equations that govern the evolution of strings on large scales. We also argue that on small scales the assumption of a local equilibrium would break down, and non-equilibrium steady states, described by the Sinai-Ruelle-Bowen distributions, should be used instead.
Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the years, which consequently led to the development of various hydrodynamic theories. In this work, we discuss the relativistic generalizations of the perturbative expansions put forward by Chapman and Enskog, and Hilbert, using general matching conditions in kinetic theory. This allows us to describe, in a comprehensive way, how different out-of-equilibrium definit…
We use principal component analysis to study the hydrodynamic attractor in Yang-Mills kinetic theory undergoing the Bjorken expansion with Color Glass Condensate initial conditions. The late time hydrodynamic attractor is characterized by a single principal component determining the overall energy scale. How it is reached is governed by the disappearance of single subleading principal component characterizing deviations of the pressure anisotropy, the screening mass and the scattering rate. We find that for wide range of couplings the approach to the hydrodynamic attractor at late times is wel…
We show how causal relativistic Navier-Stokes equations arise from the relativistic Boltzmann equation: the causality is preserved via a judicious choice of the zero modes of the collision operator. A completely analogous procedure may be used to extract causal hydrodynamics from the fluid-gravity correspondence: again, causality of the hydrodynamic equations is preserved by a suitable choice of zero modes of the corresponding differential operators in the bulk. We give examples of zero modes which give rise to causal hydrodynamic equations for non-conformal fluids with a conserved U(1) global…
We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative solution of relativistic Boltzmann equation with relaxation time approximation. We show that our results for second and third order evolution equations reduce to those of one dimensional expansion case under suitable conditions for the anisotropic parameters in Kasner space-time.
Hydro-kinetic theory of thermal fluctuations is applied to a non-conformal relativistic fluid. Solving the hydro-kinetic equations for an isotropically expanding background we find that hydrodynamic fluctuations give ultraviolet divergent contributions to the energy-momentum tensor. After shifting the temperature to account for the energy of non-equilibrium modes, the remaining divergences are renormalized into local parameters, e.g. pressure and bulk viscosity. We also confirm that the renormalization of the pressure and bulk viscosity is universal by computing them for a Bjorken expansion. T…
We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More gen…
In the framework of chiral kinetic theory (CKT), we consider a system of right- and left-handed Weyl fermions out of thermal equilibrium in a homogeneous weak magnetic field. We show that the Lorentz invariance implies a modification in the definition of the momentum current in the phase space, compared to the case in which the system is in global equilibrium. Using this modified momentum current, we derive the linearized conservation equations from the kinetic equation up to second order in the derivative expansion. It turns out that the eigenmodes of these equations, namely the hydrodynamic …
A certain identification of points in a planar Schwarzschild-anti de Sitter (AdS) black hole generates a four-dimensional static black string. In turn, a rotating black string can be obtained from a static one by means of an `illegitimate coordinate transformation', a local boost in the compact direction. On the basis of the gauge/gravity duality, these black strings are dual to rotating thermal states of a strongly interacting conformal field theory (CFT) that lives on a cylinder. In this work, we obtain the complete quasinormal mode (QNM) spectrum of the gravitational perturbations of rotati…
Under the main assumption that the axion scalar field mainly composes the dark matter in the Universe, in this paper we shall extend the formalism of kinetic axion $R^2$ gravity to include Gauss-Bonnet terms non-minimally coupled to the axion field. As we demonstrate, this non-trivial Gauss-Bonnet term has dramatic effects on the inflationary phenomenology and on the kinetic axion scenario. Specifically, in the context of our formalism, the kinetic axion ceases to be kinetically dominated at the end of the inflationary era, since the condition $\dotϕ\simeq 0$ naturally emerges in the theory. T…
On the basis of the intimate relation between Nambu dynamics and the hydrodynamics, the hydrodynamics on a non-commutative space (obtained by the quantization of space), proposed by Nambu in his last work, is formulated as ``hydrodynamics of granular material''. In Part 1, the quantization of space is done by Moyal product, and the hydrodynamic simulation is performed for the so obtained two dimensional fluid, which flows inside a canal with an obstacle. The obtained results differ between two cases in which the size of a fluid particle is zero and finite. The difference seems to come from the…
Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high degree of symmetry, suggesting the possibility of a genuine out-of-equilibrium formulation of hydrodynamics. This work demonstrates that attractor solutions also occur in non-conformal kinetic theory and spatially non-homogeneous systems, potentially having important implications for the interpretation of experimental data in heavy-ion and proton-proton col…
École polytechnique, Centre National de la Recherche Scientifique – Unité Mixte de Recherche 7644, Institut Polytechnique de Paris（巴黎综合理工学院，法国国家科学研究中心第7644联合研究单位，巴黎理工学院）；Université Libre de Bruxelles and International Solvay Institutes（布鲁塞尔自由大学和国际索尔维研究所）；Université de Mons（蒙斯大学）
Integrable hydrodynamic equations for initial chiral currents and infinite hydrodynamic chains from WZNW model and string model of WZNW type with $SU(2),$ $SO(3),$ $SP(2),$ $SU(\infty)$, $SO(\infty)$, $SP(\infty)$ constant torsions
