FIAS International Symposion on Discoveries at the Frontiers of Science, Frankfurt am Main,

Fluid Dynamics for Heavy Ions from the beginnings up to now

FIAS International Symposion on Discoveries at the Frontiers of Science, Frankfurt am Main,

June 26-30, 2017

Dedicated to

Walter Greiner

• Recent works with:

Yilong, Xie, Dujuan Wang, Horst Stöcker, Marcus Bleicher, Volodymyr Magas, Daniel Strottman and Francesco Becattini

• Dedicated to the Honor of Walter Greiner, my late colleague, mentor and friend.

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L.P. Csernai

Scheid, Ligensa, Greiner; Phys.Rev.Lett. 21 (1968) 1479, Scheid, Greiner; Z. Phys. 226 (1969) 364.

G.F. Chapline, M.H. Johnson, E. Teller, and M.S.

Weiss, Phys. Rev. D8 (1973) 135.

1973 Lake Balaton vs. Steve Koonin,

1992 NATO ASI Peniscola, E. Teller

L.P. Csernai

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EoS,

Viscosity !

… 20-30 joint publications with Walter

PICR - Varying the Number of Markers

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Pb+Pb 1.38+1.38 A TeV, b= 70 % of b_max

Lagrangian fluid cells, moving, ~ 5 mill.

MIT Bag m. EoS FO at T ~ 200 MeV, but calculated much longer, until pressure is zero for 90% of the cells.

Structure and

asymmetries of init.

state are maintained in nearly perfect

expansion.

PICR-

hydro

Quark – Gluon Plasma

• The most energetic form of matter made in laboratory

• Discovered in 2000 / 2001

• In CERN – SPS / BNL – RHIC (respectively)

• EoS  T

≈ 156 MeV ( ≈ 10

C )

• It is actually a low viscosity fluid: η/s ≈ 0.1

• Lowest among fluids; minimal at the phase transition [Csernai, Kapusta, McLerran, Phys. Rev. Lett. 2006]

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• 

• Low viscosity  strong fluctuations

• Low viscosity  dynamical instabilities

Quark – Gluon Plasma

U N I V E R S I T Y O F B E R G E N

IWoC 2014 September, Kolymbari, Crete

 Global Symmetries

 Symmetry axes in the global CM-frame:

 ( y -y)

 ( x,z -x,-z)

 Azimuthal symmetry: φ-even (cos nφ)

 Longitudinal z-odd, (rap.-odd) for v_odd

 Spherical or ellipsoidal flow, expansion

 Fluctuations

 Global flow and Fluctuations are simultaneously present  Ǝ interference

 Azimuth - Global: even harmonics - Fluctuations : odd & even harmonics

 Longitudinal – Global: v1, v3 y-odd - Fluctuations : odd & even harmonics

 The separation of Global & Fluctuating flow is a must !! (not done yet)

Peripheral Collisions (A+A)

Csernai & Stöcker, J. Phys. G: Nucl. Part. Phys. 41 (2014) 124001

Theory:

Experimen^t:

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Fluctuations Global flow

Method to compensate for C.M. rapidity fluctuations

1. Determining experimentally EbE the C.M. rapidity

2. Shifting each event to its own C.M. and evaluate flow-harmonics there

Determining EbyE the C.M. rapidity:

The rapidity acceptance of a central TPC is usually constrained (e.g for ALICE

|η| < η_lim = 0.8, and so: |η_C.M.| << η_lim , so it is not adequate for determining the C.M. rapidity of participants.

Participant rapidity from spectators

B A

C

uib.no

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ALICE: Phys. Rev. Lett. 11, 232302 (2013)

Correction, EbE

Single neutron spectators are based on nuclear multi fragmentation studies →

in experiment should be taken from data [ ALICE estimate from 1984  ]

Results from preliminary ALICE data:

Results from preliminary ALICE data show the average with EbE fluctuations considered 

v

= ~ -0.0025 v

= ~ 0

ALICE PRL 2013:

v ^odd = ~ -0.0005 v ^even = ~ -0.00025 ^{et al.}

Development of v

(y) at increasing beam energies

This can be attributed to smaller increase of p_t and the pressure, and the shorter interaction time, and also to increasing rotation.

In [Cs., Magas, Stöcker, Strottman, PRC84 (2011)] we predicted this rotation,

but the turnover depends on the balance between rotation, expansion and freeze out.

Apparently expansion is still faster and freeze out is earlier, so the turn over to the Positive side is not reached yet.

Interesting collective

flow phenomena in

low viscosity QGP 

Hot-Gluon Field  Compact IS, shear & vorticity

• [Gyulassy & Csernai, NPA460 (1986) 723]: Flux tube dominance 

• Flux tube, w/ large string tension 

• Longitudinal extension is limited:

• Energy & momentum conservation

• Shear flow, vorticity, rotation

• IS: 3-4 fm/c

• [ Magas et al., NPA 712 (2002)167]

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Viscosity vs. T has a minimum at the 1^st order phase transition. This might signal the phase transition if viscosity is measured. At lower energies this was done.

Water QGP

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ROTATION – high

η

KHI

KHI –

low η

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Kelvin – Helmholtz

Instability

Classical

Weighted Vorticity

[Csernai, Magas,Wang, Phys. Rev. C 87 (2013) 034906]

c/fm c/fm

3 c/fm !

22 [S. Schlichting, U. Washington, QM2017]

IS fluctuations in the

transverse, [x,y] - plane

[S. Schlichting, U. Washington, QM2017]

Onset of turbulence around the Bjorken flow

• Initial state Event by Event vorticity and divergence fluctuations.

• Amplitude of random vorticity and divergence fluctuations are the same

• In dynamical development viscous corrections are negligible ( no damping)

• Initial transverse expansion in the middle (±3fm) is neglected ( no damping)

• High frequency, high wave number fluctuations may feed lower wave numbers

S. Floerchinger, U.A. Wiedemann, JHEP 100,1111 (2011); J. Phys. G 38, 124171 (2011) y

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< 0.2 c/fm

!

Detecting rotation:

Lambda polarization

 From hydro

[ F. Becattini, L.P. Csernai, D.J. Wang, Phys. Rev. C 88, 034905 (2013)]

RHIC LHC

Vorticity:

!!

Consequences – vorticity (2013):

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- Will be similar to the 2001-2 I.S. in (t,z) coordinates - More compact  vorticity may survive better - The earlier results will remain qualitatively similar:

Fig. 3 The vorticity calculated in the reaction (xz) plane at t = 0.17 fm/c after

the start of fluid dynamical evolution.

Fig. 4. The dominant y component of the observable polarization, Π₀(p) in

the Λ’s rest frame.

The initial rotation can lead to observable vorticity (Fig. 3), and polarization (Fig. 4): Leading vorticity term.

The initial angular momentum can be transferred to the polarization at final state, via spin-orbit coupling or equipartition.

[L. P. Csernai, et al, PRC 87, 034906 (2013)]

[F. Becattini, et al. PRC 88, 034905 (2013)]

[F. Becattini, L.P. Csernai, and D.J. Wang, Phys. Rev. C 88, 034905 (2013)]

Based on Ref. [Becattini, 2013], Λ polarization can be calculated as:

where is the inverse temperature four-vector field. Then thermal vorticity is ω = .

Vorticity, 1st Expansion, 2nd

The polarization 3-vector in the rest frame of particle can be found by Lorentz-boosting the above four-vector:

Consequences:

Rotation and Turbulence - (2015-16)

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STAR results

[M.A. Lisa, et al. (STAR Collaboration), Invited talk, QCD Chirality Workshop - UCLA, February 23-26, 2016, Los Angeles, USA. ; QM2017 ; arXiv:1701.06657v1

Observable consequences

Mike Lisa &

STAR:

Angular mom.

Vorticity (rot v)

Λ & anti- Λ Polarization

!! Spin-Orbit interaction is different

[Yilong Xie, Dujuan Wang, and Laszlo P. Csernai PHYSICAL REVIEW C 95, 031901(R) (2017)]

x z

-y

Present parton kinetic models - HIJING, AMPT, PACIAE

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Different space-time configurations

[Long-Gang Pang, Hannah Petersen, Guang-You Qin, Victor Roy and Xin-Nian

Wang, 27 September - 3 October

2015, Kobe, Japan; and Long-Gang Pang, Hannah Petersen, Guang-You Qin, Victor

Roy, Xin-Nian Wang, arXiv: 1511.04131 ] [Wei-Tian Deng, and Xu-Guang Huang,

arXiv: 1609.01801]

Present parton kinetic models - HIJING, AMPT, PATHIA

Different space-time configurations

[Wei-Tian Deng, and Xu-Guang Huang, arXiv: 1609.01801]

ε flow ρ flow

Max ω_y is at x=0 !!!

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Initiative: new I.S. in τ, η coordinates  x,y,z,t

Thus for each streak, i, we can get the origin of the τ=τ

hyperbola,

Energy density GeV/fm ³

propagated to the

c.m. hyperbola

Consequences – vorticity (2017):

- Vorticity is max. at the edges, at high +/- X - Consequence of the Bjorken type model

- Contradicts to AMPT and parton cascade results of

[Wei-Tian Deng, and Xu-Guang Huang, arXiv: 1609.01801],

where max. is at x=0.

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Consequences – vorticity (2017):

- Vorticity in x direction is max. at the edges, at high +/- y

- The two edges point to opposite directions, +/- x, i.e. cancel in total ω

I.S. – z-directed vorticity

• I.S. : v

& v

vanish everywhere, β

& β

too

•  Initial ω

= 0  init. class. Π

=0.

• (except surface effects)

• y-directed vorticity

• Classical polarization, Π

, is negative (-y directed),

• Rel. polarization, Π

, may have small negative domains

• x-directed vorticity

• Integrated ω

= 0,  integrated class. Π

vanishes, p-dependence is symmetric.

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Relativistic corrections in the new I.S. :

The time derivative is not included in the I.S. but the gradient term,

, has finite contribution (on τ =0 hypersurface):

Just go ahead Laszlo! (IWoC2014, Kolymbari, Crete)

Consequences:

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Fig. 6 The first (left) and second (right) term of the dominant y component of the Λ polarization for momentum vectors in the transverse plane at p_z= 0,for

the FAIR U+U reaction at 8.0 GeV

 The y component is dominant, is up to ~20%, as we can compare it with x and z components later.

 1^st & 2^nd terms are opposite direction. Result into a relatively smaller value of global polarization.

Fig. 7 The first (left) and second (right) terms of the x(up) and y(down) components of the Λ polarization for momentum vectors in the transverse

plane at pz = 0,for the FAIR U+U reaction at 8.0 GeV

1. Anti-symmetry 2. Trivial.

[Becattini, et al., Eur. Phys. J. C 75, 406 (2015).] 

Consequences / c.m. !

Fig. 8 The y component (left) of polarization vector in center of mass frame and Λ’s rest frame. The right sub-figure are the modulus of the polarization in Λ’s rest frame. At FAIR, 8.0 GeV at time 2.5+4.75 fm/c.

 The modulus of polarization is very similar with the y component of polarization, both in magnitude and the structure. I. e. the other x and z components do not contribute to the

polarization, which is in line with previous observations in this work and

other papers.

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Consequences FAIR

 Similarity between y component and modulus of Polarization, in

magnitude and structure.

 Similarity between NICA and FAIR’s polarization results.

 The net polarization is still negative, which means the first term is larger

than the second term, at this time.

Fig. 9 The y component (left) and the modulus (right) of the polarization for momentum vectors in the transverse plane at pz = 0, for the NICA Au+Au reaction at

9.3 GeV. The figure is in the Λ’s rest frame.

Consequences NICA

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Polarization and EbE c.m. determination

• Earlier EbE c.m. determination  increased V

by a factor of 2 [Cs.,E.,M., (2012)].

• Now polarization in x and z directions is symmetric in EbE c.m. frame!!!

•  integrated x & z polarizations vanish (except random fluct.)

•  finding EbE c.m. is possible by

• Minimizing integrated Π

& Π

• Maximizing integrated -Π

•  Highly sensitive diagnostic tools

IWoC2014 Kolymbari, Crete

Conclusions

• Collective flow, Rotation, KHI, Turbulence are dominant in FD

• Dominant observables are expected, & seen

• QGP properties will be analyzed and Transport

properties determined quantitatively.

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