Download Transport Coefficients of Deconfined Strongly Interacting Matter: Marcus Bluhm

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Transport Coefficients
of Deconfined Strongly
Interacting Matter:
From Weak to Strong Coupling
Marcus Bluhm
SUBATECH, Nantes, France
with Burkhard Kämpfer and Krzysztof Redlich
PANIC11
MIT, Cambridge (MA), USA - 26/7/2011
Institutsname  Dr. Hans Mustermann  www.fzd.de  Mitglied der Leibniz-Gemeinschaft
Motivation – Bulk and Shear Viscosities
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system w/o conserved
charge number density
or particle-antiparticle
symmetric systems
: bulk (volume) viscosity
: shear viscosity
change in
volume BUT
constant
shape/form
change in
shape BUT
constant
volume
application of ideal hydrodynamics modelling heavy-ion collisions at RHIC and
LHC suggests at most small dissipative effects; viscous calculations confirm this
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Quasiparticle Modell (QPM)
QPM based on
➔
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- functional approach to QCD:
modell for equilibrium thermodynamics
corresponding energy-momentum tensor:
for excitations with medium-modified dispersion
relations (thermal mass)
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Effective Kinetic Theory
➔
➔
➔
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self-consistent generalization of
to non-equilibrium systems:
space-time dependence of
implies
is a functional of the distribution function
to assure basic relations: -
(Fermi liquids)
- in thermal equilibrium:
one generalizes (in case of a one-component system) to
kinetic term
potential term
closely related to effective kinetic equation of Boltzmann-Vlasov type for the
single-particle distribution function
:
➔
above conditions satisfied if
related to form of
Vlasov-term
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
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Bulk and Shear
Viscosity Coefficients
for quasiparticle systems
Institutsname  Dr. Hans Mustermann  www.fzd.de  Mitglied der Leibniz-Gemeinschaft
Bulk and Shear Viscosities
➔
decompose
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and compare w/ definition:
bulk viscosity:
shear viscosity:
cf. Chakraborty, Kapusta (2010)
& MB, Kämpfer, Redlich (2009,'10,'11)
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Bulk and Shear Viscosities
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differences: Excitations with constant vs. thermal mass
bulk viscosity:
shear viscosity:
cf. Gavin (1985)
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Relaxation Time
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collision processes relevant for shear and bulk viscosities different;
assumption: same , independent of
concentrate on SU(3): 2
2 gluon-gluon scatterings
parametrically
based on perturbative considerations
cross section depends crucially
on ratio of maximum to minimum
momentum transfer
cf. Heiselberg (1993)
parametric dependencies of pQCD results for
temperature reproduced at large
and
on coupling and
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Adjust Parameters in Thermal Equilibrium – SUc(3)
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where
Boyd et al., NPB 469 (1996)
Okamoto et al., PRD 60 (1999)
adjusted
➔
maximum around
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Quantitative Results – Specific Shear Viscosity
➔
behaviour close to
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driven by
Nakamura, Sakai, PRL 94 (2005)
Sakai, Nakamura, PoS LAT2007 221 (2007)
Meyer, PRD 76 (2007)
cf. MB, Kämpfer & Redlich (2009, 2011)
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Quantitative Results – Specific Bulk Viscosity
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Meyer, PRD 76 (2007) & PRL 100 (2008)
Meyer, NPA 830 (2009)
combined sound channel
holographic QCD,
cf. Gürsoy et al. (2009)
cf. MB, Kämpfer & Redlich (2011)
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
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Ratio of Bulk to Shear
Viscosities
Institutsname  Dr. Hans Mustermann  www.fzd.de  Mitglied der Leibniz-Gemeinschaft
Bulk to Shear Viscosity Ratio
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Big Theoretical Motivation: Viscosity coefficients in strongly
interacting Quantum Field Theories
can be deduced from Black Hole Physics
- Kovtun-Son-Starinets bound:
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Bulk to Shear Viscosity Ratio
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Big Theoretical Motivation: Viscosity coefficients in strongly
interacting Quantum Field Theories
can be deduced from Black Hole Physics
- Kovtun-Son-Starinets bound:
- similar universal bounds for other transport coefficients are unknown
BUT in some special classes of theories with holographically dual
supergravity description there exists a lower bound for the ratio
Buchel bound:
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Bulk to Shear Viscosity Ratio
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Big Theoretical Motivation: Viscosity coefficients in strongly
interacting Quantum Field Theories
can be deduced from Black Hole Physics
- Kovtun-Son-Starinets bound:
- similar universal bounds for other transport coefficients are unknown
BUT in some special classes of theories with holographically dual
supergravity description there exists a lower bound for the ratio
Buchel bound:
•
specific strongly coupled but nearly
conformal theories (AdS/CFT)
•
for scalar theory or photons in hot fluid
parametrically correct also in pQCD (weak coupling)
- might expect that there is a gradual change from one behaviour to the
other as a function of temperature
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Bulk to Shear Viscosity Ratio
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momentum integrals
quadratic dependence
Buchel's
bound
linear dependence
- at asymptotically large T:
- for
:
linear dependence on
and Buchel's bound satisfied for
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Estimating the QGP Specific Shear Viscosity
inclusion of quark degrees of freedom
by assuming that relations between
gluon and quark sector known from
perturbative regime hold close to
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leading-order estimate:
(additive)
Csernai, Kapusta, McLerran
PRL 97 (2006)
➔
mild overall increase with
; still small at
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Conclusions
•
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knowing QCD transport coefficients important for understanding
the behaviour of strongly interacting matter observed in highenergy nuclear collisions
picture: excitations with effective thermal mass
- inclusion of mean field term in energy-momentum tensor
necessary for self-consistency of the approach
- follows from kinetic equation of Boltzmann-Vlasov type
- influence of a medium-dependent effective mass in dispersion
relation minor on but prominent in
- fairly nice agreement w/ available lQCD data (SUc(3)); specific
shear viscosity as small as
- ratio of bulk to shear viscosities exhibits both quadratic and
linear dependence on conformality measure; turning point
located at the maximum in the scaled interaction measure
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
Energy Loss Parameter
relation between
and averaged transverse momentum transfer
squared per unit distance of an energetic parton
cf. Majumder, Müller, Wang (2007)
underlying assumption:
interaction between energetic parton
and medium is of same structure and
strength as interaction among thermal
excitations
Text optional: Institutsname  Prof. Hans Mustermann  www.fzd.de  Optional: Datum, etc.
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