Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.
Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical mechanisms work in the case of the scalar field model. We obtain the evolution equation for the Wigner function of a long-wavelength subsystem that describes its decoherence, isotropization, and approach to thermal equilibrium induced by interaction with short-wavelength modes. Our analysis supports the idea that decoherence, quantum-to-classical transition, and thermalization in isolated quantum systems are attributed to the experimental context, and are related to a particular procedure of decomposition of the whole quantum system into relevant and irrelevant from an observational viewpoint subsystems.
The onset of hydrodynamics in the hot medium created in relativistic heavy-ion collisions is a crucial theoretical question. A first-principle simulation requires a real-time, non-perturbative calculation of the quantum system. In this Letter, we perform such simulations using the tensor network method, which enables large-scale quantum many-body simulations by retaining only the most essential quantum states for collective behaviors. We focus on the massive Schwinger model, a low-dimensional analog of quantum chromodynamics (QCD), as they share important properties such as confinement and chiral symmetry breaking. Starting from an initial state that puts a localized excitation atop the vacuum and mimics the energy deposition from colliding nuclei, we observe hydrodynamic behavior consistent with Bjorken flow in all relevant degrees of freedom: energy density, fluid velocity, and bulk pressure. The time scale for hydrodynamic onset aligns with the thermalization time of the quantum distribution function.
Hydrodynamic phenomena seem to be ubiquitous in the universe. Hydrodynamics provides an effective, long-wavelength description of both classical and quantum systems. We study the universal spatial features of certain non-equilibrium steady states corresponding to flows of strongly correlated fluids over obstacles. We identify spatial collective modes of the strongly coupled many body system. These modes can be both hydrodynamical or non-hydrodynamical. Analytic examples can be found in the large-dimension limit of the bulk theory, but in three dimensions as well. We construct the general first-order hydrodynamic theory invariant under time translations, the Euclidean group of spatial transformations and preserving particle number. Such theories are important in many situations, from hydrodynamics of graphene to flocking behaviour of birds and motion of self-propelled organisms. We apply our non-boost invariant model of hydrodynamics to concrete flow configurations - the Poiseuille, Couette and Taylor-Couette flows. We also test the instability of the Poiseuille flow.
Nonequilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early-time preequilibrium stage of high-energy heavy-ion collisions. Besides their practical relevance they also provide a meaningful way to address the question when and to what extent a hydrodynamic description of the system becomes applicable. Within the kinetic theory framework we derive a new method to calculate time-dependent nonequilibrium Green's functions describing the evolution of energy and momentum perturbations on top of an evolving far-from-equilibrium background. We discuss the approach toward viscous hydrodynamics along with the emergence of various scaling phenomena for conformal systems. By comparing our results obtained in the relaxation time approximation to previous calculations in Yang-Mills kinetic theory, we further address the question which macroscopic features of the energy-momentum tensor are sensitive to the underlying microscopic dynamics.
Since the systems described by quantum fields are by definition extended, it is natural to think that in some limit they may reasonably well be approximated as fluids. This means that the state of the system is parameterized by a few locally well-defined fields such as temperature or energy density, obeying a set of hyperbolic equations of motion. A concrete example is the extensive use of fluid models to describe high-energy collisions [BelLan56, CarDuo73, CoFrSc74, Bjo83, CarZac83]. Our earlier derivation of quantum kinetic theory suggests a way to put this insight on a formal basis. Within its range of validity, the Boltzmann equation will drive the one-particle distribution function towards local thermal equilibrium. On scales much larger than the local thermalization scale, we expect to see hydrodynamical behavior [BeCoPa02]. This is, after all, the usual way of deriving hydrodynamics from kinetic theory [Hua87]. Beware, notwithstanding, that even at the level of classical kinetic theory there are still open questions regarding the cross-over from the kinetic to the hydro regime [KarGor02, KarGor03]. If we understand hydrodynamics as stated in the first paragraph of this chapter, then a system defined in terms of a quantum field may not have a hydrodynamic limit. This has been shown in [Elz02] for the case of a free Fermi field.
Relativistic hydrodynamics is a low-energy e↵ective theory which universally describes macroscopic behaviors of relativistic many-body systems.Its application covers the broad branches of physics such as high-energy physics, astrophysics, and condensed matter physics.Nevertheless, its derivation from underlying microscopic theories, especially from quantum field theories, has not been clearly clarified.Furthermore, it is recently pointed out that novel transport phenomena such as the chiral magnetic e↵ect, which originates from the quantum anomaly in the underlying quantum field theories, take place in the macroscopic hydrodynamic regime.In this thesis, we derive relativistic hydrodynamics from quantum field theories on the basis of the recent development of nonequilibrium statistical mechanics.In order to derive the hydrodynamic equations we introduce an assumption that the density operator is given by a local Gibbs distribution at initial time, and decompose the energy-momentum tensor and charge current into nondissipative and dissipative parts.This leads to a generalization of the Gibbs ensemble method canonically employed in equilibrium statistical mechanics.Our formalism is also applicable to the situation in the presence of the quantum anomaly, and we can describe the anomaly-induced tranport phenomena.As a basic tool of our formalism, we first develop a path integral of the thermodynamic potential for locally thermalized systems.We show microscopically that the thermodynamic pontential, which is shown to be the generating functional of systems in local thermal equilibrium, is written in terms of the quantum field theory in the curved spacetime with one imaginary-time direction.The structure of this thermally emergent curved spacetime is determined by hydrodynamic variables such as the local temperature, and fluid-four velocity, and possesses notable symmetry properties: Kaluza-Klein gauge symmetry, spatial di↵eomorphism symmetry, and gauge symmetry.With the help of the symmetry argument, we can construct the nondissipative part of the hydrodynamic equations including the anomaly-induced transport phenomena.By the use of the perturbative calculation, we evaluate the anomalous transport coe cients at one-loop level.Furthermore, we also construct a solid basis to study dissipative corrections to hydrodynamic equations.In particular, by performing the derivative expansion, together with the result on nondissipative part of the constitutive relations, we derive the firstorder dissipative hydrodynamic equations, that is, the relativistic Navier-Stokes equation.Our formalism also provides the quantum field theoretical expression of the Green-Kubo formulas for transport coe cients.iii The formulation and whole works presented from Chapter 2 to Chapter 4 are based on our original work in collaboration with Yoshimasa Hidaka (RIKEN).The work presented in Chapter 3 is in collaboration with Yoshimasa Hidaka (RIKEN), Tomoya Hayata (RIKEN), and Toshifumi Noumi (Hong Kong University of Science and Technology) [1].1 There is close investigation of priority to the Navier-Stokes equation in Ref. [11].