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Thermal features far from equilibrium: Prethermalization. Szabolcs Borsányi University of Heidelberg. different levels of equilibration is reached at different time scales; some equilbrium features appear earlier, some appear later; - PowerPoint PPT Presentation
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Thermal featuresfar from equilibrium
Prethermalization
Szabolcs BorsaacutenyiUniversity of Heidelberg
in collaboration withJ Berges C Wetterich
different levels of equilibration is reached at different time scales
some equilbrium features appear earliersome appear later
prethermalization bulk observables settle close to the final value
LTE in heavy ion collisions
How can the local equilibrium established
Present estimates for thermalization
tLTE gt 2-3 fmc
ideal hydro equations of motion
HiranoNara 2004Kolb et al
t0 = 06 fmc
Theoretical description
Classical approximation (wave dynamics)bull only low-momentum physics nonrenormalizable
nonperturbative off-shellbull classical equilibrium ne quantum equlibrium
Kinetic theories (incoherent particleparton dynamics)
bull elastic or inelastic scattering perturbative on-shell
bull problems at early times coherence gradient expansion
bull Eg pQCD parton cascade shower simulations
Resummed expansion scheme 2PI
bull Inclusion of off-shell processes
bull applicable both for early and late times
2PI resummed chiral model
bull Chiral quark model in 3+1 dimensions(two quark four scalar degree of freedom symmetric phase)
bull We solve the nonequilibrium gap equation
momentumspace
coordinatespace
Levels of equilibration
Damping Thermalization
Prethermalization
SzB Szeacutep 2000
Berges SzB Serreau 2003
Damping time
bull Initial relaxation of propagatorstime-local G(t1t2=t1p) non-local G(t1t2=0p)
bull With of the spectral function (Im )
bull No substantial evolution
bull Physical meaningndash signal loss
bull signal on top of equilibrium ensemble
bull compare decay rate to Im(p) they agree
ndash shorter than thermalization
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
LTE in heavy ion collisions
How can the local equilibrium established
Present estimates for thermalization
tLTE gt 2-3 fmc
ideal hydro equations of motion
HiranoNara 2004Kolb et al
t0 = 06 fmc
Theoretical description
Classical approximation (wave dynamics)bull only low-momentum physics nonrenormalizable
nonperturbative off-shellbull classical equilibrium ne quantum equlibrium
Kinetic theories (incoherent particleparton dynamics)
bull elastic or inelastic scattering perturbative on-shell
bull problems at early times coherence gradient expansion
bull Eg pQCD parton cascade shower simulations
Resummed expansion scheme 2PI
bull Inclusion of off-shell processes
bull applicable both for early and late times
2PI resummed chiral model
bull Chiral quark model in 3+1 dimensions(two quark four scalar degree of freedom symmetric phase)
bull We solve the nonequilibrium gap equation
momentumspace
coordinatespace
Levels of equilibration
Damping Thermalization
Prethermalization
SzB Szeacutep 2000
Berges SzB Serreau 2003
Damping time
bull Initial relaxation of propagatorstime-local G(t1t2=t1p) non-local G(t1t2=0p)
bull With of the spectral function (Im )
bull No substantial evolution
bull Physical meaningndash signal loss
bull signal on top of equilibrium ensemble
bull compare decay rate to Im(p) they agree
ndash shorter than thermalization
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
Theoretical description
Classical approximation (wave dynamics)bull only low-momentum physics nonrenormalizable
nonperturbative off-shellbull classical equilibrium ne quantum equlibrium
Kinetic theories (incoherent particleparton dynamics)
bull elastic or inelastic scattering perturbative on-shell
bull problems at early times coherence gradient expansion
bull Eg pQCD parton cascade shower simulations
Resummed expansion scheme 2PI
bull Inclusion of off-shell processes
bull applicable both for early and late times
2PI resummed chiral model
bull Chiral quark model in 3+1 dimensions(two quark four scalar degree of freedom symmetric phase)
bull We solve the nonequilibrium gap equation
momentumspace
coordinatespace
Levels of equilibration
Damping Thermalization
Prethermalization
SzB Szeacutep 2000
Berges SzB Serreau 2003
Damping time
bull Initial relaxation of propagatorstime-local G(t1t2=t1p) non-local G(t1t2=0p)
bull With of the spectral function (Im )
bull No substantial evolution
bull Physical meaningndash signal loss
bull signal on top of equilibrium ensemble
bull compare decay rate to Im(p) they agree
ndash shorter than thermalization
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
2PI resummed chiral model
bull Chiral quark model in 3+1 dimensions(two quark four scalar degree of freedom symmetric phase)
bull We solve the nonequilibrium gap equation
momentumspace
coordinatespace
Levels of equilibration
Damping Thermalization
Prethermalization
SzB Szeacutep 2000
Berges SzB Serreau 2003
Damping time
bull Initial relaxation of propagatorstime-local G(t1t2=t1p) non-local G(t1t2=0p)
bull With of the spectral function (Im )
bull No substantial evolution
bull Physical meaningndash signal loss
bull signal on top of equilibrium ensemble
bull compare decay rate to Im(p) they agree
ndash shorter than thermalization
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
Levels of equilibration
Damping Thermalization
Prethermalization
SzB Szeacutep 2000
Berges SzB Serreau 2003
Damping time
bull Initial relaxation of propagatorstime-local G(t1t2=t1p) non-local G(t1t2=0p)
bull With of the spectral function (Im )
bull No substantial evolution
bull Physical meaningndash signal loss
bull signal on top of equilibrium ensemble
bull compare decay rate to Im(p) they agree
ndash shorter than thermalization
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
SzB Szeacutep 2000
Berges SzB Serreau 2003
Damping time
bull Initial relaxation of propagatorstime-local G(t1t2=t1p) non-local G(t1t2=0p)
bull With of the spectral function (Im )
bull No substantial evolution
bull Physical meaningndash signal loss
bull signal on top of equilibrium ensemble
bull compare decay rate to Im(p) they agree
ndash shorter than thermalization
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
Nonequilibrium KMS condition
Equilibrium (KMS condition)
Out of equilibrium (generalized KMS)
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
If this relation holds for close-to-the-peak frequencies as well a Boltzmann equation may be derived from the 2PI gap equation
F and are the outcome of the dynamics Initially they were independent variables
The particle distribution is established on the damping time scale
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
Even earlier prethermalization
bull Kinetic energy kinetic temperature
Virial theorem(for weakly coupled fields)
if local equilibriumthen kinetic energy frac14 gradient energy + potential energy
This behavior has been also seen in classical field theory
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
SzB Patkoacutes Sexty 2003
Equation of state
Loss of phase informationLoss of coherencetpt Temperature = 225
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
Prethermalization is a universal far-from-equilibrium phenomenon which describes a very rapid establishment of an almost constant equation of state as well as kinetic temperature
similar behavior in Classical Field Theory(reheating after cosmological inflation)
coupling independent ldquoDephasingrdquo
SzB Patkoacutes Sexty 2003
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
Inhomogeneous ensemble
Prethermalizationbull Very early evolutionbull Far-from-equilibriumbull High occupation numbersbull Weak sensitivity to
interaction details
O(4) model withrealistic mass scales
Pretherm
lt 05 fmc
We find After Pretherm
pressure()energy() is and independent
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
What can we say for heavy ion physics
bull Assume Qs sets only the relevant scale of the early dynamics
bull Prethermalization time is coupling independent (2-25 T-1)inserting Qs for temperature scale and using a prefactor of 3
tpt frac14 06 fmc
bull After this time stable equation of state kinetic temperature
bull If we start our model with larger Yukawa coupling frac14 3Damping time Prethermalization time
Even if equilibrium is reached laterbull fluctuation dissipation (KMS) relation
bull slowly evolving spectra
bull equation of state
Even Hydrodynamics may work
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
Summary
bull Equilibration can be splitted to different stepsprethermalization damping thermalization
bull One of the scales is insensitive to coupling prethermalizationndash generic phenomenon present in various scenarios
bull After damping time nonequilibrium KMS relationbull Damping and prethermalization may coincide for
heavy ion collisions it gives about frac14 06 fmcbull This can be an ingredient to understand the
success of hydrodynamic description
