Scheffler, Sebastian Herwig Jürgen
Plasma Instabilities and Turbulence in Non-Abelian Gauge Theories.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2010)
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|Item Type:||Ph.D. Thesis|
|Title:||Plasma Instabilities and Turbulence in Non-Abelian Gauge Theories|
Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the "colour glass condensate" is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (less than approximately 1 GeV). Essential results can be translated from the gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the quasi-stationary phase following the saturation of instabilities is studied. Numerical as well as analytical calculations show that the classical time evolution drives the system towards a nonthermal fixed point which exhibits properties of turbulence. The fixed point is characterised by power-law correlation functions of the gauge field. The determined exponents 4/3 and 5/3 are identical to those found in scalar field theories, which provides indication for universality out of thermal equilibrium. Taking into account the quantum contributions in the analytical approach it is demonstrated that the full quantum theory does not possess a nonthermal fixed point at large momenta.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||QCD; Non-Abelian Gauge Theories; Quark Gluon Plasma; Heavy Ion Collisions; Thermalization; Plasma Instabilities; Turbulence; Non-equilibrium Field Theory; Lattice QCD|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 530 Physik|
|Divisions:||05 Department of Physics > Institute of Nuclear Physics|
|Date Deposited:||19 Mar 2010 10:28|
|Last Modified:||07 Dec 2012 11:56|
|Referees:||Berges, Professor Jürgen and Fischer, Professor Christian|
|Refereed:||17 February 2010|