Strongly coupled plasma - hydrodynamics, thermalization and - - PowerPoint PPT Presentation
Strongly coupled plasma - hydrodynamics, thermalization and nonequilibrium behavior Romuald A. Janik Jagiellonian University Krakw work with M. Heller, P. Witaszczyk see RJ 1311.3966 [hep-ph] for a recent review 1 / 22 Outline Why use
Jagiellonian University Kraków
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◮ New ways of looking at nonperturbative gauge theory physics... ◮ Intricate links with General Relativity... ◮ Has been extended to many other cases
3 / 22
◮ New ways of looking at nonperturbative gauge theory physics... ◮ Intricate links with General Relativity... ◮ Has been extended to many other cases
3 / 22
◮ New ways of looking at nonperturbative gauge theory physics... ◮ Intricate links with General Relativity... ◮ Has been extended to many other cases
3 / 22
◮ New ways of looking at nonperturbative gauge theory physics... ◮ Intricate links with General Relativity... ◮ Has been extended to many other cases
3 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
4 / 22
◮ QCD plasma produced at RHIC/LHC is most probably a strongly
◮ Nonperturbative methods applicable to real time dynamics are very
◮ Conventional lattice QCD is inherently Euclidean
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◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
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◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ Deconfined phase ◮ Strongly coupled ◮ No supersymmetry!
◮ No running coupling −
◮ (Exactly) conformal equation of state −
◮ No confinement/deconfinement phase transition −
6 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
◮ The applicability of using N = 4 plasma to model real world
◮ Use it as a theoretical laboratory where we may compute from ‘first
◮ Gain qualitative insight into the physics which is very difficult to
◮ Discover some universal properties? (like η/s) ◮ For N = 4 plasma the AdS/CFT correspondence is technically
◮ Use the results on strong coupling properties of N = 4 plasma as a
◮ Eventually one may consider more realistic theories with AdS/CFT
7 / 22
αβdxαdxβ
αβR − 6 g 5D αβ = 0
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αβdxαdxβ
αβR − 6 g 5D αβ = 0
8 / 22
αβdxαdxβ
αβR − 6 g 5D αβ = 0
8 / 22
αβdxαdxβ
αβR − 6 g 5D αβ = 0
8 / 22
αβdxαdxβ
αβR − 6 g 5D αβ = 0
8 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
◮ Asymptotics of gµν(xρ, z) at z ∼ 0 gives the
◮ We can test whether Tµν(xρ) is of a
◮ We can check for local thermal equilibrium ◮ The area of the apparent horizon defines for
◮ We observe some initial entropy
9 / 22
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◮ In a conformal theory, T µ µ = 0 and ∂µT µν = 0 determine, under the
◮ The longitudinal and transverse pressures are then given by
◮ The assumptions of symmetry fix uniquely the flow velocity
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◮ In a conformal theory, T µ µ = 0 and ∂µT µν = 0 determine, under the
◮ The longitudinal and transverse pressures are then given by
◮ The assumptions of symmetry fix uniquely the flow velocity
11 / 22
◮ In a conformal theory, T µ µ = 0 and ∂µT µν = 0 determine, under the
◮ The longitudinal and transverse pressures are then given by
◮ The assumptions of symmetry fix uniquely the flow velocity
11 / 22
◮ In a conformal theory, T µ µ = 0 and ∂µT µν = 0 determine, under the
◮ The longitudinal and transverse pressures are then given by
◮ The assumptions of symmetry fix uniquely the flow velocity
11 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ Structure of the analytical result for large τ:
4 3 −
1 2 3 3 4
8 3 +−3 + 2π2 + 24 log 2 − 24 log2 2
1 2 3 1 4
10 3 +. . .
◮ Leading term — perfect fluid behaviour
◮ In general:
∞
2n 3
◮ Currently we know 240 terms in this expansion
◮ The hydrodynamic series is only asymptotic and has zero radius of
12 / 22
◮ In order to study far-from equilibrium behaviour for small τ we have
◮ We get rid of the dependence on the number of degrees of freedom
c π2T 4 eff (τ) ◮ Previously, we normalized our initial data by setting
◮ It is much better to fix the normalization through the hydrodynamic
1 3 in the τ → ∞ limit
13 / 22
◮ In order to study far-from equilibrium behaviour for small τ we have
◮ We get rid of the dependence on the number of degrees of freedom
c π2T 4 eff (τ) ◮ Previously, we normalized our initial data by setting
◮ It is much better to fix the normalization through the hydrodynamic
1 3 in the τ → ∞ limit
13 / 22
◮ In order to study far-from equilibrium behaviour for small τ we have
◮ We get rid of the dependence on the number of degrees of freedom
c π2T 4 eff (τ) ◮ Previously, we normalized our initial data by setting
◮ It is much better to fix the normalization through the hydrodynamic
1 3 in the τ → ∞ limit
13 / 22
◮ In order to study far-from equilibrium behaviour for small τ we have
◮ We get rid of the dependence on the number of degrees of freedom
c π2T 4 eff (τ) ◮ Previously, we normalized our initial data by setting
◮ It is much better to fix the normalization through the hydrodynamic
1 3 in the τ → ∞ limit
13 / 22
◮ In order to study far-from equilibrium behaviour for small τ we have
◮ We get rid of the dependence on the number of degrees of freedom
c π2T 4 eff (τ) ◮ Previously, we normalized our initial data by setting
◮ It is much better to fix the normalization through the hydrodynamic
1 3 in the τ → ∞ limit
13 / 22
◮ In order to study far-from equilibrium behaviour for small τ we have
◮ We get rid of the dependence on the number of degrees of freedom
c π2T 4 eff (τ) ◮ Previously, we normalized our initial data by setting
◮ It is much better to fix the normalization through the hydrodynamic
1 3 in the τ → ∞ limit
13 / 22
◮ Very clear transition to a hydrodynamic behaviour ◮ Very little information on the initial energy density at τ = 0 (unless
14 / 22
◮ Very clear transition to a hydrodynamic behaviour ◮ Very little information on the initial energy density at τ = 0 (unless
14 / 22
◮ Very clear transition to a hydrodynamic behaviour ◮ Very little information on the initial energy density at τ = 0 (unless
14 / 22
◮ Very clear transition to a hydrodynamic behaviour ◮ Very little information on the initial energy density at τ = 0 (unless
14 / 22
◮ Very clear transition to a hydrodynamic behaviour ◮ Very little information on the initial energy density at τ = 0 (unless
14 / 22
◮ Very clear transition to a hydrodynamic behaviour ◮ Very little information on the initial energy density at τ = 0 (unless
14 / 22
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◮ Is there a simple phenomenological model simpler than 5D Einstein’s
◮ Can we get information on the possible (number of) degrees of
19 / 22
◮ Is there a simple phenomenological model simpler than 5D Einstein’s
◮ Can we get information on the possible (number of) degrees of
19 / 22
◮ Is there a simple phenomenological model simpler than 5D Einstein’s
◮ Can we get information on the possible (number of) degrees of
19 / 22
◮ Is there a simple phenomenological model simpler than 5D Einstein’s
◮ Can we get information on the possible (number of) degrees of
19 / 22
◮ Is there a simple phenomenological model simpler than 5D Einstein’s
◮ Can we get information on the possible (number of) degrees of
19 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ On the gravity side, deviations from hydrodynamics may be
◮ Each quasinormal mode represents an independent degree of
◮ The generic structure of QNM modes for a boost-invariant flow
◮ One can estimate that s =
0 πT(τ)dτ at the transition to
◮ It turns out that s = 1.6...3 and Im ωQNM = 2.75, 4.76, 6.77, ... ◮ A few additional DOF might suffice?
20 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ The scalar dof corresponds to a scalar QNM with frequencies
◮ Key feature: the frequencies have only very mild dependence on
◮ We may write the equation of motion in a generic hydrodynamic flow
I + ω2 R
21 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22
◮ AdS/CFT provides a very general framework for studying
◮ The AdS/CFT methods do not presuppose hydrodynamics so are
◮ AdS/CFT may fill in gaps in our knowledge of the early
◮ Thermalization = hydrodynamization ◮ Simple dimensionless criterion for applicability of hydrodynamics ◮ Important role of ‘initial entropy’ as a characterization of the initial
◮ One can perhaps understand better the dynamics of lowest
◮ Key role of quasinormal frequencies...
22 / 22