Feld, Steffen: Relativistic freeze out studies and two-particle Correlations. 2019
Inhalt
- Heavy-Ion Collisions
- Acknowledgments
- What is seen in such experiments
- Where are heavy-ion collisions performed
- What are the recent questions
- Relativistic Boltzmann equation in polar Milne coordinates for modeling kinetic freeze out
- Declaration of authorship
- Motivation
- Geometry
- Preparation
- Relativistic Boltzmann equation in polar Milne coordinates
- Relativistic drift term in polar Milne coordinates
- Free streaming
- Balance equations or Collision integrals
- Relaxation time approximation
- Role of the Jüttner distribution
- Closing remark
- The steady state free streaming solution
- Interlude Hydrodynamics
- Moments of the distribution function
- Ideal Hydrodynamics
- Viscous Hydrodynamics
- Anisotropic Hydrodynamics
- Hydrodynamics including sources
- Moments of the anisotropic free streaming solution for massless particles
- Useful substitutions
- Moments of the massless anisotropic free streaming distribution Ffs
- 0th-moment of the free streaming distribution Ffs (x, pi)
- 1st-moment of the free streaming distribution Ffs (x, pi) wrt. p
- 1st-moment of the free streaming distribution Ffs (x, pi) wrt. pr
- 2nd-moment of the free streaming distribution Ffs (x, pi) wrt. p
- 2nd-moment of the free streaming distribution Ffs (x, pi) wrt. pr
- 2nd-moment of the free streaming distribution Ffs (x, pi) wrt. p
- 2nd-moment of the free streaming distribution Ffs (x, pi) wrt. ps
- Comments
- Evolution of the pressure components
- Computing the moments of the anisotropic equilibrium distribution for massive particles
- Useful substitution and useful functions
- 1st-moment of the free streaming distribution Ffs (x, pi) wrt. p
- 1st-moment of the free streaming distribution Ffs (x, pi) wrt. pi
- 2nd-moment of the free streaming distribution Ffs (x, pi) wrt. p
- Numerical computation of the 2nd-moments of the free streaming distribution Ffs (x, pi)
- Remarks
- Physical observables for the distribution Ffs (x, pi)
- Particle spectrum from an isotropic fluid
- Particle spectrum from Ffs (x, pi)
- Anisotropic flow coefficients vn
- Anisotropic flow coefficients vn from an isotropic fluid
- Anisotropic flow coefficients vn from Ffs (x, pi)
- Discussion and outlook
- Era of last rescatterings
- Computing the different moments of the massless Boltzmann equation within 1st linearization
- 0th-moment of the Boltzmann-equation in RTA
- 1st-moment wrt p of the Boltzmann-equation in RTA
- 1st-moment wrt p of the Boltzmann-equation in RTA
- 1st-moment wrt ps of the Boltzmann-equation in RTA
- 1st-moment wrt pr of the Boltzmann-equation in RTA
- 2nd-moment wrt p of the Boltzmann-equation in RTA
- 2nd-moment wrt p of the Boltzmann-equation in RTA
- 2nd-moment wrt ps of the Boltzmann-equation in RTA
- 2nd-moment wrt pr of the Boltzmann-equation in RTA
- Remarks
- Closing the equations via 2nd-linearization
- Computing the moments of the dissipative, massless correction to the free-streaming solution
- 0th-moment of f
- 1st-moment of f wrt p
- 1st-moment of f wrt pr
- 1st-moment of f wrt p
- 2nd-moment of f wrt p
- 2nd-moment of f wrt pr
- 2nd-moment of f wrt p
- Discussion and outlook
- Azimuthally dependent two-particle correlations
- Introduction
- On the way to two-particle distributions
- Controlling the background
- Fluctuations of {vn}
- Physical origin of {vn} fluctuations
- Linearization of {vn} fluctuations
- Power law like fluctuations
- Extraction of fluctuations from a Glauber Monte Carlo
- How do the fluctuations of vn influence fluctuations of vpairn,c/s
- Summary and Outlook