# Browsing by Author "Mueller, Berndt"

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Item Unknown Applications of Gauge/Gravity Duality in Heavy Ion Collisions(2014) Yang, Di-LunIn order to analyze the strongly interacting quark gluon plasma in heavy ion collisions, we study different probes by applying the gauge/gravity duality to facilitate our qualitative understandings on such a non-perturbative system. In this dissertation, we utilize a variety of holographic models to tackle many problems in heavy ion physics including the rapid thermalization, jet quenching, photon production, and anomalous effects led by external electromagnetic fields. We employ the AdS-Vaidya metric to study the gravitational collapse corresponding to the thermalization of a strongly coupled gauge theory, where we compute the approximated thermalization time and stopping distances of light probes in such a non-equilibrium medium. We further generalize the study to the case with a nonzero chemical potential. We find that the non-equilibrium effect is more influential for the probes with smaller energy. In the presence of a finite chemical potential, the decrease of thermalization times for both the medium and the light probes is observed.

On the other hand, we also investigate the anisotropic effect on the stopping distance related to jet quenching of light probes and thermal-photon production. The stopping distance and photoemission rate in the anisotropic background depend on the moving directions of probes.

The influence from a magnetic field on photoemission is as well investigated in the framework of the D3/D7 system, where the contributions from massive quarks are involved. The enhancement of photon production for photons generated perpendicular to the magnetic field is found. Given that the mass of massive quarks is close to the critical embedding, the meson-photon transition will yield a resonance in the spectrum. We thus evaluate flow coefficient $v_2$ of thermal photons in a 2+1 flavor strongly interacting plasma. The magnetic-field induced photoemission results in large $v_2$ and the resonance from massive quarks gives rise to a mild peak in the spectrum. Moreover, we utilize Sakai-Sugimoto model to analyze the chiral electric separation effect, where an axial current is generated parallel to the applied electric field in the presence of both the vector and axial chemical potentials. Interestingly, the axial conductivity is approximately proportional to the product of the vector chemical potential and the axial chemical potential for arbitrary magnitudes of the chemical potentials.

Item Unknown Entropy production and equilibration in Yang-Mills quantum mechanics(2011) Tsai, Hung-MingEntropy production in relativistic heavy-ion collisions is an important physical quantity for studying the equilibration and thermalization of hot matters of quantumchromodynamics (QCD). To formulate a nontrivial definition of entropy for an isolated quantum system, a certain kind of coarse graining may be applied so that the entropy for this isolated quantum system depends on time explicitly. The Husimi distribution, which is a coarse grained distribution in the phase space, is a suitable candidate for this approach. We proposed a general and systematic method of solving the equation of motion of the Husimi distribution for an isolated quantum system. The Husimi distribution is positive (semi-)definite all over the phase space. In this method, we assume the Husimi distribution is composed of a large number of Gaussian test functions. The equation of motion of the Husimi distribution, formulated as a partial differential equation, can be transformed into a system of ordinary differential equations for the centers and the widths of these Gaussian test functions. We numerically solve the system of ordinary differential equations for the centers and the widths of these test functions to obtain the Husimi distribution asa function of time. To ensure the numerical solutions of the trajectories of the test particles preserve physical conservation laws, we obtain a constant of motion for the quantum system. We constructed a coarse grained Hamiltonian whose expectation value is exactly conserved. The conservation of the coarse grained energy confirms the validity of this method. Moreover, we calculated the time evolution of the coarse grained entropy for a model system (Yang-Mills quantum mechanics). Yang-Mills quantum mechanics is a quantum system whose classical correspondence possesses chaotic behaviors. The numerical results revealed that the coarse grained entropy for Yang-Mills quantum mechanics saturates to a value that coincides with the micro-canonical entropy corresponding to the energy of the system. Our results confirmed the validity of the framework of first-principle evaluation of the coarse grained entropy growth rate. We show that, in the energy regime under study, the relaxation time for the entropy production in Yang-Mills quantum mechanics is approximately the same as the characteristic time of the system, indicating fast equilibration of the system. Fast equilibration of Yang-Mills quantum mechanics is consistent to current understanding of fast equilibration of hot QCD matter in relativistic heavy-ion collisions.Item Open Access The Response of Hot QCD Matter to Hard Partons(2009) Neufeld, Richard BryonThe quark gluon plasma (QGP) forms when matter governed by quantum chromodynamics (QCD) undergoes a transition at high temperature or high density from hadronic bound states to deconfined quarks and gluons. The QGP at high temperature is believed to be experimentally accessible in relativistic heavy-ion collisions, such as those done at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Lab and in the near future at the Large Hadron Collider (LHC) at CERN. The results obtained so far reveal the production of energetic (hard) partons in the early stages of a heavy-ion collision which propagate through the plasma. Results also show that the QGP produced at RHIC is a nearly ideal fluid and that hard partons may generate conical, Mach-like, disturbances in the QGP.

This thesis uses theoretical methods to address how the QGP responds to a hard parton that propagates through the plasma and contains the first rigorous derivation of how a hard parton deposits energy and momentum in a QGP which lead to the formation of a Mach cone. A comparison of experimental results with the theory introduced in this thesis could shed light on important properties of the QGP such as its equation of state and transport coefficients like viscosity. I investigate this problem by evaluating the source of energy and momentum generated by the hard parton in the QGP. Formalisms are developed and applied for evaluating the source of energy and momentum in perturbation theory with three different methods: classical kinetic theory, finite temperature field theory, and by including the energy lost by the hard parton to radiation. Having obtained the source of energy and momentum generated by the hard parton, I evaluate the medium response using linearized hydrodynamics. My results show Mach cone formation in the medium. I compare the medium response for different viscosities and speeds of sound, from which I find the Mach cone weakens and broadens as viscosity is increased. By studying the time evolution of the medium response once the source of energy and momentum is turned off, which occurs in a heavy-ion collision during the hadronic phase, I find that the conical disturbance is enhanced relative to diffusive contributions over a time period of several fm/c.