FIAS Scientific Report 2011 - Frankfurt Institute for Advanced Studies ...

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Aspects of transport coefficients in relativistic hydrodynamics Collaborators: X. G. Huang 1,2 , P. Huovinen 1,2 , K. Kodama 3 , T. Koide 1,3 , D. H. Rischke 1,2 , A. Sedrakian 2 1 Frankfurt Institute for Advanced Studies, 2 Institute for Theoretical Physics, Frankfurt, Germany 3 Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil Relativistic hydrodynamics is one of the most often used approaches in studying the collective phenomena in heavy-ion collisions, supernova explosions, and neutron stars. However, including viscosities in the relativistic hydrodynamics is not easy. A naive relativistic generalization of Navier-Stokes theory does not work, because it violates causality and is usually unstable, and hence does not permit numerical simulations. A solution to this problem has been known since works of Mueller, and Israel and Stewart more than 30 years ago, and the resulting theory is usually called second-order hydrodynamics. Different from Navier-Stokes theory where the viscous stress tensors Π and π µν are completely fixed by the distribution of velocity fields, in second-order hydrodynamics, Π and π µν are treated as independent dynamical variables which should be solved simultaneously with the velocity fields. As was proven, second-order hydrodynamics is causal and stable, but the cost is the appearance of new transport coefficients. The microscopic formulas for the shear viscosity η, the bulk viscosity ζ and corresponding relaxation times τπ and τΠ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potential by using the projection operator method. The nontriviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition of the bulk viscous pressure. We show that, when the operator definition for the bulk viscous pressure Π is appropriately chosen, the leading order result of the ratio of ζ and τΠ coincides with the same ratio obtained at vanishing chemical potential. In applying these formulae to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. Quarks produced in the early stage of non-central heavy-ion collisions could develop a global spin polarization along the opposite direction of the reaction plane due to the spin-orbital coupling via parton interaction in a medium that has finite longitudinal flow shear along the direction of the impact parameter. We study how such polarization evolves via multiple scattering in a viscous quark-gluon plasma with an initial laminar flow. The final polarization is found to be sensitive to the viscosity and the initial shear of local longitudinal flow. Relativistic magnetohydrodynamics of strongly magnetized relativistic fluids is derived in the ideal and dissipative cases, taking into account the breaking of spatial symmetries by a quantizing magnetic field. A complete set of transport coefficients, consistent with the Curie and Onsager principles, is derived for thermal conduction, as well as shear and bulk viscosities. It is shown that in the most general case the dissipative function contains five shear viscosities, two bulk viscosities, and three thermal conductivity coefficients. We use Zubarev’s non-equilibrium statistical operator method to relate these transport coefficients to correlation functions of equilibrium theory. The desired relations emerge at linear order in the expansion of the non-equilibrium statistical operator with respect to the gradients of relevant statistical parameters (temperature, chemical potential, and velocity.) The transport coefficients are cast in a form that can be conveniently computed using equilibrium (imaginary-time) infrared Green’s functions defined with respect to the equilibrium statistical operator. Related publications in 2011: 1) X. -G. Huang, P. Huovinen and X. -N. Wang, Quark polarization in a viscous quark-gluon plasma, Phys. Rev. C84, 054910 (2011) 2) X. -G. Huang, A. Sedrakian and D. H. Rischke, Kubo formulas for relativistic fluids in strong magnetic fields, Annals Phys. 326, 3075 (2011) 3) X. -G. Huang and T. Koide, Shear viscosity, bulk viscosity and relaxation times of causal dissipative relativistic fluid-dynamics at finite temperature and chemical potential, arXiv:1105.2483 [hep-th] 4) X. -G. Huang, T. Kodama, T. Koide and D. H. Rischke, Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics, Phys. Rev. C83, 024906 (2011) 42
Chiral hadronic model including resonances Collaborators: Philip Rau 1,2 , Jan Steinheimer 1 , Stefan Schramm 1 , Horst Stöcker 1,3 1 FIAS, 2 Institut für Theoretische Physik, Goethe Universität Frankfurt, 3 GSI - Helmholtzzentrum für Schwerionen- forschung, Darmstadt. We extended the existing effective chiral flavour SU(3) model for the QCD equation of state which was developed in Frankfurt over the last years to include all hadronic resonances up to masses of m ≤ 2.6 GeV. All particles are coupled to the scalar σ-field and the vector ω-field. We introduce a parameter rv controlling the coupling strength to the repulsive vector fields and thus primarily affecting the particles’ abundancies. Therefore, by varying rv we are able to study the impact of heavier resonances on the phase diagram of strongly interacting matter with particular interest on the chiral phase transition. By studying the thermodynamic properties of our model we observe a good agreement to latest continuum extrapolated lattice data if we chose a physically reasonable vector coupling close to one. This finding is supported by our results for the susceptibilities of conserved charges on the phase transition which are again comparable to lattice QCD for rv ∼ 1. However, in this case our model rules out a first order phase transition in favour of a smooth cross over transition not only at vanishing baryochemical potentials µB = 0 but in the whole µB-regime ruling out the postulated existence of a critical end point. T [MeV] 200 180 160 140 120 100 isentropes, r v =0.9 5A GeV 10A GeV 20A GeV 30A GeV 40A GeV 80 60 40 20 0 0 isentropes for EoS with rv =0.9 200 400 600 PT line for rv =0.4 PT at T=0 for rv =0.8 rv =1.0 800 1000 1200 1400 1600 1800 µ B [MeV] χ s /T 2 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 r s = 0.97, µ B = 0 int. HRG HRG p4, N τ = 8 asqtad, N τ =12 hisq, N τ =8 stout, cont. 130 140 150 160 170 180 190 200 210 220 T [MeV] a): QCD phase diagram from our model with isentropes for various beam energies for a vector coupling rv ∼ 1 where there is only a broad crossover phase transition. The shown phase transition line depicts the situation for the lowest reasonable coupling strength rv = 0.4. b): Strange quark susceptibility from our model at µB = 0 (blue dashed line) compared to lattice QCD results from various lattice actions. Good agreement is obtained with latest continuum extrapolated data up to the critical temperature Tc. Related publications in 2011: 1) P. Rau, J. Steinheimer, S. Schramm and H. Stöcker, Baryon resonances in a chiral hadronic model for the qcd equation of state, arXiv:1109.3621 [hep-ph], accepted by Phys. Rev. C. 2) P. Rau, J. Steinheimer, S. Schramm and H. Stöcker, Resonance states in an effective chiral hadronic model, arXiv:1201.3834 [hep-ph]. 43
Page 1 and 2: FIAS Scientific Report 2011
Page 3: FIAS Scientific Report 2011 Table o
Page 6 and 7: Physics Research highlights 2011 To
Page 9 and 10: 1. Partner Research Centers 9
Page 11 and 12: ExtreMe Matter Institute EMMI by Ca
Page 13 and 14: Bernstein Focus Neurotechnology Fra
Page 15 and 16: 2. Graduate Schools 15
Page 17 and 18: participants reported on their proj
Page 19 and 20: Courses offered at FIGSS Summer Sem
Page 21 and 22: 3. FIAS Scientific Life 21
Page 23 and 24: 28.07.2011 Prof. Dr. Victor Flambau
Page 25 and 26: Conferences and meetings (co)organi
Page 27 and 28: 4. Research Reports 4.1 Nuclear Phy
Page 29 and 30: Hydrodynamics of a quark droplet Co
Page 31 and 32: Production of hyper-nuclei in react
Page 33 and 34: On production and properties of mul
Page 35 and 36: Monte Carlo modeling microdosimetry
Page 37 and 38: Monte Carlo simulation of the spall
Page 39 and 40: Dimuon radiation within a (3+1)d hy
Page 41: Initial state anisotropies and thei
Page 45 and 46: Trace anomaly and the vector coupli
Page 47 and 48: Dileptons from the strongly interac
Page 49 and 50: Space-time evolution of the magneti
Page 51 and 52: Extreme isospin in heavy nuclei Col
Page 53 and 54: Production of heavy and superheavy
Page 55 and 56: The phase diagram in T -µB-Nc spac
Page 57 and 58: Critical Zeeman Fields for Unitary
Page 59 and 60: BCS-BEC Crossover in 2D Fermi Gases
Page 61 and 62: Applications of a chiral SU(3) mode
Page 63 and 64: The phase diagram of black holes in
Page 65 and 66: Black holes in short scale modified
Page 67 and 68: Fractal dimensions and micro-struct
Page 69 and 70: Untangling the interactions between
Page 71 and 72: Stimulus information coded by spike
Page 73 and 74: Non-stationarity of neuronal activi
Page 75 and 76: Timescale of information processing
Page 77 and 78: Discovery of agency in 6 and 8-mont
Page 79 and 80: Power spectra of the natural input
Page 81 and 82: Self-organization in recurrent neur
Page 83 and 84: Learning mechanisms underlying visu
Page 85 and 86: Emerging Bayesian priors in a self-
Page 87 and 88: Non-linear generative models and th
Page 89 and 90: Preference elicitation and Bayesian
Page 91 and 92: 4.3 Biology, Chemistry, Molecules,
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DNA unzipping Collaborators: S.N. V
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Statistical mechanics of protein fo
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Phase transitions in large clusters
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Photo-processes in fullerenes and e
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Assessment of complex DNA damage Co
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Novel light sources: Crystalline un
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Monte-Carlo code for channeling dyn
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Programs for many-body descriptions
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Are 12 C radiation effects in liver
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Objective identification of residue
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Structural basis for the dual RNA-r
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The ALICE High Level Trigger Collab
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Arithmetic over Galois fields on mo
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High Performance GPU-based DGEMM an
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How stable are transport model resu
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5. Talks and Publications 123
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Conference and Seminar Talks 2011
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Conference and Seminar Talks 2011 W
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FIAS conference abstracts and poste
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FIAS conference abstracts and poste
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FIAS Publications 2011 - Journal pu
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FIAS publications 2011 - Conference
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FIAS publications 2011 - Patents 24
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The success of FIAS would not have
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