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<p>The 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. </p><p>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.</p>
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