We derive transport equations for fermions and bosons in spatially or temporally varying backgrounds with special symmetries, by use of the Schwinger-Keldysh formalism. In a noninteracting theory the coherence information is shown to be encoded in new singular shells for the 2-point function. Imposing this phase space structure to the interacting theory leads to a a self-consistent equation of motion for a physcial density matrix, including coherence and a well defined collision integral. The method is applied e.g. to demonstrate how an initially coherent out-of-equlibrium state approaches equlibrium through decoherence and thermalization.
In this thesis we develop a novel approximation scheme (eQPA), where the effects of nonlocal coherence are included in the kinetic approach to nonequilibrium quantum dynamics. The key element in our formalism is the finding of new singular shell solutions, located at $k_{0,z} = 0$ in the phase space of 2-point Wightman function, which describe the nonlocal quantum coherence between the ``opposite'' mass-shell excitations for spatially homogeneous and static planar symmetric problems, respectively. This phase space structure leads to a closed set of transport equations for the corresponding on-…
I review what is required to compute transport coefficients in ultra-relativistic, weakly coupled gauge theories, at leading order in $g$, using kinetic theory. Then I discuss how the calculation would look in alternative approaches: the 2PI method, and direct diagrammatic analysis. I argue that the 2PI method may be a good way to derive the kinetic theory, but is not very useful directly (in a gauge theory). The diagrammatic approach is almost hopeless.
The evaluation of hydrodynamic transport coefficients in relativistic field theory, and the emergence of an effective kinetic theory description, is examined. Even in a weakly-coupled scalar field theory, interesting subtleties arise at high temperatures where thermal renormalization effects are important. In this domain, a kinetic theory description in terms of the fundamental particles ceases to be valid, but one may derive an effective kinetic theory describing excitations with temperature dependent properties. While the shear viscosity depends on the elastic scattering of typical excitatio…
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries, quantum coherence manifests itself in the form of new spectral solutions for the dynamical 2-point correlation function. This spectral structure leads to a consistent approximation for dynamical equations that describe coherent evolution in presence of decohering collisions. We illustrate the method by solving the bosonic Klein problem and the bound states fo…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation is finding new spectral solutions for the 2-point Green's functions written in the Wigner representation, that are carrying the information of the quantum coherence. Physically observable density matrix is then defined from the bare singular 2-point function by convoluting it with the extrenous information about the state of the system. The formalism is shown…
We discuss the kinetics of a disoriented chiral condensate, treated as an open quantum system. We suggest that the problem is analogous to that of a damped harmonic oscillator. Master equations are used to establish a hierarchy of relevant time scales. Some phenomenological consequences are briefly outlined.
According to the Kubo formulas we employ the (3+1)-d parton cascade, Boltzmann approach of multiparton scatterings (BAMPS), to calculate the anisotropic transport coefficients (shear viscosity and electric conductivity) for an ultrarelativistic Boltzmann gas in the presence of a magnetic field. The results are compared with those recently obtained by using the Grad's approximation. We find good agreements between both results, which confirms the general use of the derived Kubo formulas for calculating the anisotropic transport coefficients of quark-gluon plasma in a magnetic field.
We study the three-dimensional transport theory of massive spin-1/2 fermions resulting from the vorticity dependent quantum kinetic equation. This quantum kinetic equation has been introduced to take account of noninertial properties of rotating coordinate frames. We show that it is the appropriate relativistic kinetic equation which provides the vorticity dependent semiclassical transport equations of the three-dimensional Wigner function components. We establish the semiclassical kinetic equations of a linearly independent set of components. By means of them, kinetic equations of the chiral …
The transport coefficients of causal relativistic dissipative fluid dynamics are calculated both in a field-theoretical and a kinetic approach. We find that the results from the traditional kinetic calculation by Israel and Stewart are modified. The new expressions for the viscous transport coefficients agree with the results obtained in the field-theoretical approach when the contributions from pair creation and annihilation are neglected.
Minijet thermalization and jet transport coefficients in QCD kinetic theory
SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS)（SUBATECH UMR 6457（IMT大西洋学院，南特大学，IN2P3/法国国家科学研究中心））；Institute of Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）；MIT Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Institute for Theoretical Physics, University of Heidelberg（海德堡大学理论物理研究所）
In Weyl semimetals subjected to torsion, there are two different kinds of chirality: i) the (coordinate-space) shape of the twisted crystal is chiral, and ii) the momentum space contains chiral quasi-particles. Here we construct a general kinetic theory of anomalous transport using the phase space (coordinate and momentum spaces combined) Berry curvature induced by torsion in Weyl systems. We describe how torsion generates the chiral chemical potential, and thus leads to the Chiral Magnetic Effect (CME) in the presence of a background magnetic field. We propose to measure the CME current induc…
We derive field-theoretic local quantum transport equations which can describe quantum coherence. Our methods are based on Kadanoff--Baym equations derived in the Schwinger--Keldysh closed time path formalism of non-equilibrium quantum field theory. We focus on spatially homogeneous and isotropic systems and mixing fermions with a time-dependent mass and a weak coupling to a thermal plasma. We introduce a new local approximation (LA) method and use it to derive quantum kinetic equations which can describe coherence and also include effects of the spectral width. The method is based on a local …
We derive the quantum kinetic theory for fermions with arbitrary mass in a background electromagnetic field from the Wigner-function approach. Since spin of massive fermions is a dynamical degree of freedom, the kinetic equations with the leading-order quantum corrections describe entangled dynamics of not only the vector- and axial-charge distributions but also of the spin polarization. Therefore, we obtain one scalar and one axial-vector kinetic equations with magnetization currents pertinent to the spin-orbit interaction. We show that our results smoothly reduce to the massless limit where …
We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is found to arise from new spectral solutions for the dynamical 2-point correlation function in the mean field limit. The physical density matrix $ρ$ and its dynamics is shown to be necessarily dependent on the extrenous information on the system, and expressions that relate $ρ$ to fundamental coherence functions and fermionic particle and antiparticle numbers …
We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has a form of a linearized kinetic equation as usual, but our formalism enables us to incorporate higher-order corrections of the coupling systematically for the first time. Furthermore, it is clarified that the higher-order corrections are nicely summarized into that of the vertex function, spectral function, and collision term. We identify the diagrams up to the next-to-next-leading order corrections i…
Within the real-time formulation of nonequilibrium field theory, generalized transport equations are derived avoiding the standard quasiparticle approximation. They permit to include unstable particles into the transport scheme. In order to achieve a self-consistent, conserving and thermodynamically consistent description, we generalize the Baym's $Φ$-functional method to genuine nonequilibrium processes. The developed transport description naturally includes all those quantum features already inherent in the corresponding equilibrium limit. Memory effects appearing in collision term diagrams …
We derive the quantum kinetic equations for massive and massless quarks coupled with the background chromo-electromagnetic fields from the Wigner-function approach with the $\hbar$ expansion and effective power-counting scheme. For each case, one obtains coupled color-singlet and color-octet kinetic equations, which also involve the scalar and axial-vector components for the charge and spin transport. These kinetic equations delineate entangled evolution of the corresponding distribution functions decomposed in color space. At weak coupling, we derive the close form of the color-singlet kineti…
We developed a new general-relativistic quantum-kinetics neutrino transport code, GRQKNT, for numerical studies of quantum kinetics of non-equilibrium neutrinos in six-dimensional phase space. This code is intended for use in both local and global simulations of neutrino transport in core-collapse supernova and binary neutron star merger. It has been widely recognized that global simulations of collective neutrino oscillations, in particular fast neutrino-flavor conversions (FFC), require unfeasible computational resources due to large disparity of scales between flavor conversion and astrophy…
