Quantum transport with memory effects

1
Quantum transport with memory effects

• Björn Schenke and Carsten Greiner
• Institut für Theoretische Physik
• Johann Wolfgang Goethe-Universität, Frankfurt
• EM-Probes of Strongly Interacting Matter - ECT -
  Trento
• June 22nd 2007

2
Motivation

• Do the properties of quantum mechanical particles
  adjust to the medium immediately or do they have
  some memory of the past?
• In particular Is the quasi-stationary
  approximation valid when describing vector mesons
  in an evolving medium?
• Do memory effects affect the dilepton yields in
  heavy ion collisions?
• What are the important time scales for this
  particular scenario?

medium
medium
?
3
Motivation II
Fig.2 Taken from E. Scomparins (NA60) talk
_at_QM2005 Published in PRL96 - 2006
Fig.1 J.P.Wessels et al. Nucl.Phys. A715,
262-271 (2003)
Need medium modifications of the ?-meson to
explain data. These modifications happen
dynamically in a HIC and we use real time quantum
field theory to determine how fast the mesons
adjust to the changing medium
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Motivation III
medium modifications
thermal equilibrium
(quasi-stationary hypothesis)
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Realtime formalism

• Lets first calculate the time dependent
  spectral function of a vector meson
• from fundamental quantum mechanics without
  approximations
• For that we apply the realtime formalism (for
  non-stationary systems the
• Gell-Mann and Low theorem does not apply)
• Expectation values of operators are
  calculated along a time contour

Greens function with time arguments on
the contour
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Equations of motion

• Dyson equations for the contour Greens function

with self energy and

• From these we can derive the Kadanoff-Baym
  equations using
• and fixing the time arguments at opposite sides
  of the contour.

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Equations of motion II

• Kadanoff-Baym equations

and the hermitian conjugates.
memory
nonlocal in time ? include memory

• For the retarded and advanced propagators

they yield the equations of motion
and the hermitian conjugates.
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Interpretation of Greens functions

• if one does a Wigner transformation ? phase
  space distribution

? Boltzmann equation, semi-classical transport,

• spectral information

• for example

• noninteracting, homogeneous situation

• interacting, homogeneous equilibrium situation

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Can we see the memory?

• Before calculating dilepton yields, first
  consider
• the vector mesons spectral function
• Its memory is visible in the retarded propagator

Example Perform a mass change over time from
400 MeV to 770 MeV and look at the retarded
propagator after the change is finished.
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Spectral function of the omega

• Time evolution of the spectral function of the
  omega meson during a change of the mass and the
  width (within 8 fm/c) compared to the
  quasi-static case

Red Dynamical quantum case Green quasi static
case
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Time scales

• Introduce time dependence like

e.g. from these differences we retrieve a
timescale
At this point compare
time scale , with
c2-3.5 c depends on initial width and mass
?-meson retardation of about 3 fm/c

• The behavior of the ? becomes adiabatic on
  timescales much larger than 3 fm/c
• Hence we can expect an effect in HICs since
  changes happen on 6 fm/c

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Nonequilibrium dilepton rate
B. Schenke and C. Greiner, Phys.Rev. C73034909,
2006 - hep-ph/0509026

• We start from the Kadanoff-Baym equations

• Do not make a first order gradient expansion

• Project on the lepton number in

• Dynamical dilepton rate

memory
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Dilepton rate in two-time rep.
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Dropping mass scenario
B. Schenke and C. Greiner, Phys.Rev.Lett.
98022301 (2007)

• Chiral symmetry restoration ? dropping meson
  masses

• ?-meson spectral function during fireball
  evolution

• Spectral function enters dilepton rate

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Observable Dilepton yield

• Different parameterizations
• Also include additional broadening by about 100
  MeV
• Calculate for momentum k0-1.5 GeV
• Expanding Firecylinder model for NA60 scenario
• yields V(t), T(t) and n(t)
• Total yield per invariant mass M

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Comparison
B. Schenke and C. Greiner, Phys.Rev.Lett.
98022301 (2007)

• Compare to static calculation without memory

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Comparison

• Compare to static calculation without memory

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Coupling to N-hole states

• Coupling of the ? to N(1520)
• Broadening of the ? to G700 MeV
• Broadening of the resonance to 400 MeV
• Constant ?-mass

• Memory effects are less dramatic
• More distinct structure in dynamic
• calculation

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Coupling to N-hole states

• Coupling of the ? to N(1520)
• Broadening of the ? to G700 MeV
• Broadening of the resonance to 400 MeV

• Memory effects are less dramatic
• More distinct structure in dynamic
• calculation

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Summary and conclusion

• Found memory effects for meson spectral functions
  in a dynamically evolving medium as in a HIC
• Calculated dilepton yields from fireball within
• equilibrium and nonequilibrium description
• Found increased yield in nonequilibrium case
• by a factor of about 3-4 and differences in
  shape for the Brown-Rho scaling scenarios only
  about 30 difference for the melted spectral
  function
• The rho meson has a memory of the medium!
• Quantum transport leads to different results
  than the quasi-static approximation this study
  allows for quantification of the error made by
  using that approximation depends on time
  scales!