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The quark-gluon plasma produced in heavy-ion collisions at RHIC and LHC is a hot and dense state of strongly correlated matter. It behaves like an almost-perfect fluid featuring a small ratio of shear viscosity to entropy density. In this thesis we calculate within a two-flavor Nambu--Jona-Lasinio model the shear viscosity as function of temperature and chemical potential. A new Kubo formula is developed, incorporating the full Dirac structure of the quark spectral function and avoiding commonly used on-shell approximations. Mesonic fluctuations occurring at Fock level provide the dominant dissipative process. The resulting parameter-free ratio is an overall decreasing function of temperature and chemical potential. In combination with hard-thermal-loop results we find this ratio to feature a minimum slightly above the AdS/CFT benchmark.

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Robert Lang ( 1986) studied physics (2005) and mathematics (2006) at the Technische Universität München where he graduated in both subjects with distinction. In 2011 he deepened his studies on the strong interaction and non-equilibrium thermodynamics under the supervision of Prof. Dr. W. Weise. In 2015 he obtained his Ph.D. in theoretical physics.

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