Skip to main content
SpringerLink
Log in

Dynamical Evolution of Heavy-Ion Collisions

  • Chapter
  • First Online:
Properties of QCD Matter at High Baryon Density

Abstract

Relativistic viscous hydrodynamics and transport models are the primary tools to study the real-time dynamics of relativistic nuclear collisions. At high collision energies, the hybrid approach that combines hydrodynamics with hadronic transport achieves quantitative descriptions of many experimental observables across different systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For illustrative purpose, we only show the approximate expression here. See Ref. [122] and references therein for more details.

References

  1. Mohanty B (2011) STAR experiment results from the beam energy scan program at RHIC. J Phys G 38:124023. arXiv: 1106.5902

  2. Luo X, Xu N (2017) Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview. Nucl Sci Tech 28(8):112. arXiv: 1701.02105

  3. Adamczyk L et al (2017) bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program. Phys Rev C 96(4):044904. arXiv: 1701.07065

  4. Keane D (2017) The beam energy scan at the relativistic heavy ion collider. J Phys: Conf Ser 878(1):012015

    Google Scholar 

  5. Stephanov MA (2011) On the sign of kurtosis near the QCD critical point. Phys Rev Lett 107:052301. arXiv: 1104.1627

  6. Bzdak A, Esumi S, Koch V, Liao J, Stephanov M, Xu N (2020) Mapping the phases of quantum chromodynamics with beam energy scan. Phys Rep 853:1–87. arXiv: 1906.00936

  7. Karpenko IA, Huovinen P, Petersen H, Bleicher M (2015) Estimation of the shear viscosity at finite net-baryon density from \(A+A\) collision data at \(\sqrt{s_{\rm NN}} = 7.7-200\) GeV. Phys Rev C 91(6):064901. arXiv: 1502.01978

  8. Shen C, Schenke B (2018) Dynamical initial state model for relativistic heavy-ion collisions. Phys Rev C 97(2):024907. arXiv: 1710.00881

  9. Lin Z-W (2018) Extension of the Bjorken energy density formula of the initial state for relativistic heavy ion collisions. Phys Rev C 98(3):034908. arXiv: 1704.08418

  10. Gale C, Jeon S, McDonald S, Paquet J-F, Shen C (2019) Photon radiation from heavy-ion collisions in the \(\sqrt{s_{NN}}=19-200\) GeV regime. Nucl Phys A 982:767–770. arXiv: 1807.09326

  11. Mendenhall T, Lin Z-W (2021) Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness. Phys Rev C 103(2):024907. arXiv: 2012.13825

  12. Shen C, Yan L (2020) Recent development of hydrodynamic modeling in heavy-ion collisions. Nucl Sci Tech 31(12):122. arXiv: 2010.12377

  13. Denicol GS, Gale C, Jeon S, Monnai A, Schenke B, Shen C (2018) Net baryon diffusion in fluid dynamic simulations of relativistic heavy-ion collisions. Phys Rev C 98(3):034916. arXiv:1804.10557

  14. Li M, Shen C (2018) longitudinal dynamics of high baryon density matter in high energy heavy-ion collisions. Phys Rev C 98(6):064908. arXiv: 1809.04034

  15. Mohs J, Ryu S, Elfner H (2020) Particle production via strings and baryon stopping within a hadronic transport approach. J Phys G 47(6):065101. arXiv:1909.05586

  16. Bjorken JD (1983) Highly relativistic nucleus-nucleus collisions: the central rapidity region. Phys Rev D 27:140–151

    Article  Google Scholar 

  17. Adcox K et al (2005) Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: experimental evaluation by the PHENIX collaboration. Nucl Phys A 757:184–283 nucl-ex/0410003

    Article  Google Scholar 

  18. Oliinychenko D, Petersen H (2016) Deviations of the energy-momentum tensor from equilibrium in the initial state for hydrodynamics from transport approaches. Phys Rev C 93(3):034905. arXiv: 1508.04378

  19. Okai M, Kawaguchi K, Tachibana Y, Hirano T (2017) New approach to initializing hydrodynamic fields and mini-jet propagation in quark-gluon fluids. Phys Rev C 95(5):054914. arXiv: 1702.07541

  20. Lin Z-W, Ko CM, Li B-A, Zhang B, Pal S (2005) A Multi-phase transport model for relativistic heavy ion collisions. Phys Rev C 72:064901. arXiv:nucl-th/0411110

  21. Nara Y, Otuka N, Ohnishi A, Niita K, Chiba S (2000) Study of relativistic nuclear collisions at AGS energies from p + Be to Au + Au with hadronic cascade model. Phys Rev C 61:024901. arXiv:nucl-th/9904059

  22. Weil J et al (2016) Particle production and equilibrium properties within a new hadron transport approach for heavy-ion collisions. Phys Rev C 94(5):054905. arXiv:1606.06642

  23. Bass SA et al (1998) Microscopic models for ultrarelativistic heavy ion collisions. Prog Part Nucl Phys 41:255–369. arXiv: nucl-th/9803035

  24. Bleicher M et al (1999) Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model. J Phys G 25:1859–1896 hep-ph/9909407

    Article  Google Scholar 

  25. Cassing W, Bratkovskaya EL (2009) Parton-hadron-string dynamics: an off-shell transport approach for relativistic energies. Nucl Phys A 831:215–242. arXiv: 0907.5331

  26. Buss O, Gaitanos T, Gallmeister K, van Hees H, Kaskulov M, Lalakulich O, Larionov AB, Leitner T, Weil J, Mosel U (2012) Transport-theoretical description of nuclear reactions. Phys Rep 512:1–124 arXiv: 1106.1344

  27. Pang L, Wang Q, Wang X-N (2012) Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics. Phys Rev C 86:024911. arXiv: 1205.5019

  28. Shen C, Denicol G, Gale C, Jeon S, Monnai A, Schenke B (2017) A hybrid approach to relativistic heavy-ion collisions at the RHIC BES energies. Nucl Phys A 967:796–799. arXiv:1704.04109

  29. Du L, Heinz U, Vujanovic G (2019) Hybrid model with dynamical sources for heavy-ion collisions at BES energies. Nucl Phys A 982:407–410. arXiv:1807.04721

  30. Akamatsu Y, Asakawa M, Hirano T, Kitazawa M, Morita K, Murase K, Nara Y, Nonaka C, Ohnishi A (2018) Dynamically integrated transport approach for heavy-ion collisions at high baryon density. Phys Rev C 98(2):024909. arXiv:1805.09024

  31. Shen C, Schenke B (2018) Initial state and hydrodynamic modeling of heavy-ion collisions at RHIC BES energies. PoS CPOD2017:006. arXiv: 1711.10544

  32. Bialas A, Bzdak A, Koch V (2018) Stopped nucleons in configuration space. Acta Phys Polon B 49:103. arXiv:1608.07041

  33. Shen C, Alzhrani S (2020) Collision-geometry-based 3D initial condition for relativistic heavy-ion collisions. Phys Rev C 102(1):014909. arXiv:2003.05852

  34. Kharzeev D (1996) Can gluons trace baryon number? Phys Lett B 378:238–246. arXiv: nucl-th/9602027

  35. Shen C, Schenke B (2019) Dynamical initialization and hydrodynamic modeling of relativistic heavy-ion collisions. Nucl Phys A 982:411–414. arXiv:1807.05141

  36. Wang X-N, Gyulassy M (1991) HIJING: a Monte Carlo model for multiple jet production in p p, p A and A A collisions. Phys Rev D 44:3501–3516

    Article  Google Scholar 

  37. Andersson B, Gustafson G, Ingelman G, Sjostrand T (1983) Parton fragmentation and string dynamics. Phys Rep 97:31–145

    Google Scholar 

  38. Zhang B, Ko CM, Li B-A, Lin Z-W (2000) A multiphase transport model for nuclear collisions at RHIC. Phys Rev C 61:067901. arXiv:nucl-th/9907017

  39. Lin Z-W, Pal S, Ko CM, Li B-A, Zhang B (2001) Charged particle rapidity distributions at relativistic energies. Phys Rev C 64:011902. arXiv: nucl-th/0011059

  40. Zhang B (1998) ZPC 1.0.1: A Parton cascade for ultrarelativistic heavy ion collisions. Comput Phys Commun 109:193–206. arXiv:nucl-th/9709009

  41. Lin Z-W, Ko CM (2002) Partonic effects on the elliptic flow at RHIC. Phys Rev C 65:034904. arXiv:nucl-th/0108039

  42. Lin Z-W (2014) Evolution of transverse flow and effective temperatures in the parton phase from a multi-phase transport model. Phys Rev C 90(1):014904

    Google Scholar 

  43. Pang L-G, Petersen H, Qin G-Y, Roy V, Wang X-N (2016) Decorrelation of anisotropic flow along the longitudinal direction. Eur Phys J A 52(4):97. arXiv:1511.04131

  44. Andersson B, Gustafson G, Soderberg B (1983) A general model for jet fragmentation. Z Phys C 20:317

    Google Scholar 

  45. Petersen H, Steinheimer J, Burau G, Bleicher M, Stocker H (2008) A fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage. Phys Rev C 78:044901. arXiv:0806.1695

  46. Werner K (2007) Core-corona separation in ultra-relativistic heavy ion collisions. Phys Rev Lett 98:152301. arXiv:0704.1270

  47. Steinheimer J, Bleicher M (2011) Core-corona separation in the UrQMD hybrid model. Phys Rev C 84:024905. arXiv:1104.3981

  48. Kanakubo Y, Okai M, Tachibana Y, Hirano T (2018) Enhancement of strange baryons in high-multiplicity proton–proton and proton–nucleus collisions. PTEP 2018(12):121D01. arXiv:1806.10329

  49. Kanakubo Y, Tachibana Y, Hirano T (2020) Unified description of hadron yield ratios from dynamical core-corona initialization. Phys Rev C 101(2):024912. arXiv:1910.10556

  50. Bertsch GF, Kruse H, Gupta SD (1984) Boltzmann equation for heavy ion collisions. Phys Rev C 29:673–675. [Erratum: Phys. Rev. C 33, 1107–1108 (1986)]

    Google Scholar 

  51. Bertsch GF, Das Gupta S (1988) A Guide to microscopic models for intermediate-energy heavy ion collisions. Phys Rep 160:189–233

    Google Scholar 

  52. Cassing W, Metag V, Mosel U, Niita K (1990) Production of energetic particles in heavy ion collisions. Phys Rep 188:363–449

    Article  Google Scholar 

  53. Welke GM, Prakash M, Kuo TTS, Das Gupta S, Gale C (1988) Azimuthal distributions in heavy ion collisions and the nuclear equation of state. Phys Rev C 38:2101–2107

    Google Scholar 

  54. Gale C, Welke GM, Prakash M, Lee SJ, Das Gupta S (1990) Transverse momenta, nuclear equation of state, and momentum-dependent interactions in heavy-ion collisions. Phys Rev C 41:1545–1552

    Google Scholar 

  55. Aichelin J, Stoecker H (1986) Quantum molecular dynamics. A Novel approach to N body correlations in heavy ion collisions. Phys Lett B 176:14–19

    Google Scholar 

  56. Aichelin J (1991) ‘Quantum’ molecular dynamics: a Dynamical microscopic n body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions. Phys Rep 202:233–360

    Google Scholar 

  57. Sorge H, Stoecker H, Greiner W (1989) Poincare invariant hamiltonian dynamics: modeling multi - hadronic interactions in a phase space approach. Ann Phys 192:266–306

    Google Scholar 

  58. Sorge H (1995) Flavor production in Pb (160-A/GeV) on Pb collisions: effect of color ropes and hadronic rescattering. Phys Rev C 52:3291–3314. arXiv:nucl-th/9509007

  59. Maruyama T, Niita K, Maruyama T, Chiba S, Nakahara Y, Iwamoto A (1996)Relativistic effects in the transverse flow in the molecular dynamics framework. Prog Theor Phys 96:263–268. arXiv:nucl-th/9601010

  60. Isse M, Ohnishi A, Otuka N, Sahu PK, Nara Y (2005) Mean-field effects on collective lows in high-energy heavy-ion collisions from AGS to SPS energies. Phys Rev C 72:064908. arXiv:nucl-th/0502058

  61. Ko CM, Li Q, Wang R-C (1987) Relativistic Vlasov equation for heavy ion collisions. Phys Rev Lett 59:1084–1087

    Google Scholar 

  62. Ko C-M, Li Q (1988) Relativistic Vlasov-Uehling-Uhlenbeck model for heavy-ion collisions. Phys Rev C 37:2270–2273

    Article  Google Scholar 

  63. Li Q, Wu JQ, Ko CM (1989) Relativistic Vlasov-Uehling-Uhlenbeck equation for nucleus-nucleus collisions. Phys Rev C 39:849–852

    Article  Google Scholar 

  64. Elze HT, Gyulassy M, Vasak D, Heinz H, Stoecker H, Greiner W (1987) Towards a relativistic selfconsistent quantum transport theory of hadronic matter. Mod Phys Lett A 2:451–460

    Google Scholar 

  65. Blattel B, Koch V, Cassing W, Mosel U (1988) Covariant Boltzmann-Uehling-Uhlenbeck approach for heavy-ion collisions. Phys Rev C 38:1767–1775

    Article  Google Scholar 

  66. Blaettel B, Koch V, Mosel U (1993) Transport theoretical analysis of relativistic heavy ion collisions. Rep Prog Phys 56:1–62

    Article  Google Scholar 

  67. Fuchs C, Wolter HH (1995) The Relativistic Landau-Vlasov method in heavy ion collisions. Nucl Phys A 589:732–756

    Article  Google Scholar 

  68. Fuchs C, Lehmann E, Sehn L, Scholz F, Kubo T, Zipprich J, Faessler A (1996) Heavy ion collisions and the density dependence of the local mean field. Nucl Phys A 603:471–485

    Article  Google Scholar 

  69. Nara Y, Stoecker H (2019) Sensitivity of the excitation functions of collective flow to relativistic scalar and vector meson interactions in the relativistic quantum molecular dynamics model RQMD.RMF. Phys Rev C 100(5):054902. arXiv:1906.03537

  70. Nara Y, Maruyama T, Stoecker H (2020) Momentum-dependent potential and collective flows within the relativistic quantum molecular dynamics approach based on relativistic mean-field theory. Phys Rev C 102(2):024913. arXiv:2004.05550

  71. Li B-A, Ko CM (1998) Probing the softest region of nuclear equation of state. Phys Rev C 58:1382–1384. arXiv:nucl-th/9807088

  72. Danielewicz P, Gossiaux PB, Lacey RA (1999) Hadronic transport model with a phase transition. Fundam Theor Phys 95:69–84. arXiv:nucl-th/9808013

  73. Danielewicz P (1999) Nuclear phase transitions in transport theory. In: 27th international workshop on the gross properties of nuclei and nuclear excitations (Hirschegg 99), pp 263–272. arXiv:nucl-th/9902043

  74. Sorensen A, Koch V (2021) Phase transitions and critical behavior in hadronic transport with a relativistic density functional equation of state. Phys Rev C 104(3):034904. arXiv:2011.06635

  75. Kim M, Jeon S, Kim Y-M, Kim Y, Lee C-H (2020) Extended parity doublet model with a new transport code. Phys Rev C 101(6):064614. arXIv:2006.02023

  76. Halbert EC (1981) Density patterns and energy-angle distributions from a simple cascade scheme for last Ne-20 + U-238 collisions. Phys Rev C 23:295–330

    Article  Google Scholar 

  77. Gyulassy M, Frankel KA, Stoecker H (1982) Do nuclei flow at high-energies? Phys Lett B 110:185–188

    Google Scholar 

  78. Kahana DE, Keane D, Pang Y, Schlagel T, Wang S (1995) Collective flow from the intranuclear cascade model. Phys Rev Lett 74:4404–4407. arXiv:nucl-th/9405017

  79. Nara Y, Niemi H, Ohnishi A, Stöcker H (2016) Examination of directed flow as a signature of the softest point of the equation of state in QCD matter. Phys Rev C94(3):034906. arXiv:1601.07692

  80. Sorge H (1999) Highly sensitive centrality dependence of elliptic flow: a novel signature of the phase transition in QCD. Phys Rev Lett 82:2048–2051. arXiv: nucl-th/9812057

  81. Nara Y, Niemi H, Steinheimer J, Stöcker H (2017) Equation of state dependence of directed flow in a microscopic transport model. Phys Lett B 769:543–548. arXiv:1611.08023

  82. Nara Y, Niemi H, Ohnishi A, Steinheimer J, Luo X, Stöcker H (2018) Enhancement of elliptic flow can signal a first order phase transition in high energy heavy ion collisions. Eur Phys J A 54(2):18. arXIv: 1708.05617

  83. Nara Y, Steinheimer J, Stoecker H (2018) The enhancement of v\(_{4}\) in nuclear collisions at the highest densities signals a first-order phase transition. Eur Phys J A 54(11):188. arXiv:1809.04237

  84. He Y, Lin Z-W (2017) Improved quark coalescence for a multi-phase transport model. Phys Rev C 96(1):014910. arXiv: 1703.02673

  85. Zhang L-Y, Chen J-H, Lin Z-W, Ma Y-G, Zhang S (2018) Two-particle angular correlations in \(pp\) and \(p\)-Pb collisions at energies available at the CERN Large Hadron Collider from a multiphase transport model. Phys Rev C 98(3):034912. arXiv:1808.10641

  86. Borsanyi S, Fodor Z, Hoelbling C, Katz SD, Krieg S, Szabo KK (2014) Full result for the QCD equation of state with 2+1 flavors. Phys Lett B 730:99–104. arXiv:1309.5258

  87. Bazavov A et al (2014) Equation of state in ( 2+1 )-flavor QCD. Phys Rev D 90:094503. arXiv:1407.6387

  88. Monnai A, Schenke B, Shen C (2019) Equation of state at finite densities for QCD matter in nuclear collisions. Phys Rev C 100(2):024907. arXiv:1902.05095

  89. Noronha-Hostler J, Parotto P, Ratti C, Stafford JM (2019) Lattice-based equation of state at finite baryon number, electric charge and strangeness chemical potentials. Phys Rev C 100(6):064910. arXiv: 1902.06723

  90. Monnai A, Schenke B, Shen C (2021) QCD Equation of state at finite chemical potentials for relativistic nuclear collisions. 1. arXiv:2101.11591

  91. Denicol GS, Niemi H, Molnar E, Rischke DH (2012) Derivation of transient relativistic fluid dynamics from the Boltzmann equation. Phys Rev D 85:114047. arXiv:1202.4551. [Erratum: Phys. Rev. D 91, 039902 (2015)]

  92. Denicol GS, Jeon S, Gale C (2014) Transport coefficients of bulk viscous pressure in the 14-moment approximation. Phys Rev C 90(2):024912 1403.0962

    Article  Google Scholar 

  93. Greif M, Fotakis JA, Denicol GS, Greiner C (2018) Diffusion of conserved charges in relativistic heavy ion collisions. Phys Rev Lett 120(24):242301. arXiv:1711.08680

  94. Rose J-B, Greif M, Hammelmann J, Fotakis JA, Denicol GS, Elfner H, Greiner C (2020) Cross-conductivity: novel transport coefficients to constrain the hadronic degrees of freedom of nuclear matter. Phys Rev D 101(11):114028. arXiv:2001.10606

  95. Fotakis JA, Greif M, Greiner C, Denicol GS, Niemi H (2020) Diffusion processes involving multiple conserved charges: a study from kinetic theory and implications to the fluid dynamical modeling of heavy ion collisions. Phys Rev D 101(7):076007. arXiv:1912.09103

  96. Ivanov YB, Russkikh VN, Toneev VD (2006) Relativistic heavy-ion collisions within 3-fluid hydrodynamics: Hadronic scenario. Phys Rev C 73:044904. arXiv:nucl-th/0503088

  97. Batyuk P, Blaschke D, Bleicher M, Ivanov YuB, Karpenko I, Merts S, Nahrgang M, Petersen H, Rogachevsky O (2016) Event simulation based on three-fluid hydrodynamics for collisions at energies available at the Dubna Nuclotron-based Ion Collider Facility and at the Facility for Antiproton and Ion Research in Darmstadt. Phys Rev C 94:044917. arXiv:1608.00965

  98. Petersen H (2014) Anisotropic flow in transport + hydrodynamics hybrid approaches. J Phys G 41(12):124005 1404.1763

    Google Scholar 

  99. Pratt S (2014) Accounting for backflow in hydrodynamic-Boltzmann interfaces. Phys Rev C 89(2):024910 1401.0316

    Article  Google Scholar 

  100. Oliinychenko D, Huovinen P, Petersen H (2015) Systematic investigation of negative cooper-frye contributions in heavy ion collisions using coarse-grained molecular dynamics. Phys Rev C 91(2):024906 1411.3912

    Article  Google Scholar 

  101. Schwarz C, Oliinychenko D, Pang LG, Ryu S, Petersen H (2018) Different realizations of Cooper–Frye sampling with conservation laws. J Phys G 45(1):015001. arXiv:1707.07026

  102. Oliinychenko D, Koch V (2019) Microcanonical particlization with local conservation laws. Phys Rev Lett 123(18):182302. arXiv:1902.09775

  103. Oliinychenko D, Shi S, Koch V (2020) Effects of local event-by-event conservation laws in ultrarelativistic heavy-ion collisions at particlization. Phys Rev C 102(3):034904. arXiv:2001.08176

  104. Vovchenko V, Koch V (2020) Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions. 12 2020. arXiv:2012.09954

  105. Stoecker H, Greiner W (1986) High-energy heavy ion collisions: probing the equation of state of highly excited hadronic matter. Phys Rept 137:277–392

    Google Scholar 

  106. Pang L-G, Zhou K, Su N, Petersen H, Stöcker H, Wang X-N (2018) An equation-of-state meter of quantum chromodynamics transition from deep learning. Nat Commun 9(1):210. arXiv:1612.04262

  107. Du Y-L, Zhou K, Steinheimer J, Pang L-G, Motornenko A, Zong H-S, Wang X-N, Stöcker H (2020) Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning. Eur Phys J C 80(6):516. arXiv:1910.11530

  108. Steinheimer J, Pang L, Zhou K, Koch V, Randrup J, Stoecker H (2019) A machine learning study to identify spinodal clumping in high energy nuclear collisions. JHEP 12:122. arXiv:1906.06562

  109. Fupeng LI, Yongjia WANG, Qingfeng LI (2020) Using deep learning to study the equation of state of nuclear matter. Nucl Phys Rev 37(4):825–832

    Google Scholar 

  110. Wang R, Ma Y-G,Wada R, Chen L-W, HeW-B, Liu H-L, Sun K-J (2020) Nuclear liquid-gas phase transition with machine learning. Phys Rev Res 2(4):043202. arXiv:2010.15043

  111. Huang Y, Pang L-G, Luo X, Wang X-N (2022) Probing criticality with deep learning in relativistic heavy-ion collisions. Phys Lett B 827:137001. arXiv:2107.11828

  112. Pratt S, Sangaline E, Sorensen P, Wang H (2015) Constraining the eq. of state of super-hadronic matter from heavy-ion collisions. Phys Rev Lett 114:202301. arXiv:1501.04042

  113. Stephanov MA, Rajagopal K, Shuryak EV (1998) Signatures of the tricritical point in QCD. Phys Rev Lett 81:4816–4819. arXiv:hep-ph/9806219

  114. Stephanov MA, Rajagopal K, Shuryak EV (1999) Event-by-event fluctuations in heavy ion collisions and the QCD critical point. Phys Rev D 60:114028. arXiv:hep-ph/9903292

  115. Berdnikov B, Rajagopal K (2000) Slowing out-of-equilibrium near the QCD critical point. Phys Rev D 61:105017 hep-ph/9912274

    Article  Google Scholar 

  116. Grossi E, Soloviev A, Teaney D, Yan F (2020) Transport and hydrodynamics in the chiral limit. Phys Rev D 102(1):014042. arXiv:2005.02885

  117. Grossi E, Soloviev A, Teaney D, Yan F (2021) Soft pions and transport near the chiral critical point. 1. arXiv:2101.10847

  118. Akamatsu Y, Mazeliauskas A, Teaney D (2017) A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion. Phys Rev C 95(1):014909. arXiv:1606.07742

  119. Landau LD, Lifšic EM, Lifshitz EM, P L, Pitaevskii LP, Sykes JB, Kearsley MJ (1980) Statistical physics: theory of the condensed state. Course of theoretical physics. Elsevier Science

    Google Scholar 

  120. Kapusta JI, Muller B, Stephanov M (2012) Relativistic theory of hydrodynamic fluctuations with applications to heavy ion collisions. Phys Rev C85:054906. arXiv:1112.6405

  121. Akamatsu Y, Mazeliauskas A, Teaney D (2018) Bulk viscosity from hydrodynamic fluctuations with relativistic hydrokinetic theory. Phys Rev C 97(2):024902. arXiv:1708.05657

  122. Stephanov M, Yin Y (2018) Hydrodynamics with parametric slowing down and fluctuations near the critical point. Phys Rev D98(3):036006. arXiv:1712.10305

  123. Akamatsu Y, Teaney D, Yan F, Yin Y (2018) Transits of the QCD Critical Point. 1811:05081

    Google Scholar 

  124. Martinez M, Schäfer T (2019) Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid. Phys Rev C 99(5):054902. arXiv:1812.05279

  125. An X, Başar G, Stephanov M, Yee H-U (2020) Fluctuation dynamics in a relativistic fluid with a critical point. Phys Rev C 102(3):034901. arXiv:1912.13456

  126. An X, Basar G, Stephanov M, Yee H-U (2020) Evolution of non-Gaussian hydrodynamic fluctuations. 9. arXiv:2009.10742

  127. Pratt S, Plumberg C (2019) Evolving charge correlations in a hybrid model with both hydrodynamics and hadronic boltzmann descriptions. Phys Rev C 99(4):044916. arXiv:1812.05649

  128. Pratt S, Plumberg C (2020) Determining the diffusivity for light quarks from experiment. Phys Rev C 102(4):044909. arXiv:1904.11459

  129. Crossley M, Glorioso P, Liu H (2017) Effective field theory of dissipative fluids. JHEP 1709:095. arXiv:1511.03646

  130. Crossley M, Glorioso P, Liu H (2017) Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current. JHEP 1709:096. arXiv:1701.07817

  131. Liu H, Glorioso P (2018) Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics. PoS, TASI2017:008. arXiv:1805.09331

  132. Chen-Lin X, Delacrétaz LV, Hartnoll SA (2019) Theory of diffusive fluctuations. Phys Rev Lett 122(9):091602. arXiv:1811.12540

  133. Delacretaz LV, Glorioso P (2020) Breakdown of diffusion on chiral edges. Phys Rev Lett 124(23):236802. arXiv:2002.08365

  134. Mukherjee S, Venugopalan R, Yin Y (2015) Real time evolution of non-Gaussian cumulants in the QCD critical regime. Phys Rev C 92(3):034912. arXiv:1506.00645

  135. Yin Y (2018) The QCD critical point hunt: emergent new ideas and new dynamics. 11. arXiv:1811.06519

  136. Zurek WH (1996) Cosmological experiments in condensed matter systems. Phys Rep 276:177–221. arXiv:cond-mat/9607135

  137. Mukherjee S, Venugopalan R, Yin Y (2016) Universal off-equilibrium scaling of critical cumulants in the QCD phase diagram. Phys Rev Lett 117(22):222301. arXiv:1605.09341

  138. Rajagopal K, Ridgway G, Weller R, Yin Y (2020) Understanding the out-of-equilibrium dynamics near a critical point in the QCD phase diagram. Phys Rev D 102(9):094025. arXiv:1908.08539

  139. Du L, Heinz U, Rajagopal K, Yin Y (2020) Fluctuation dynamics near the QCD critical point. 4. arXiv:2004.02719

  140. Martinez M, Schäfer T, Skokov V (2019) Critical behavior of the bulk viscosity in QCD. Phys Rev D 100(7):074017. arXiv:1906.11306

  141. Nahrgang M, Bluhm M, Schaefer T, Bass SA (2019) Diffusive dynamics of critical fluctuations near the QCD critical point. Phys Rev D 99(11):116015. arXiv:1804.05728

  142. Sogabe N, Yamamoto N, Yin Y (2021) Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media. 5. arXiv:2105.10271

  143. Jia J (2014) Event-shape fluctuations and flow correlations in ultra-relativistic heavy-ion collisions. J Phys G 41(12):124003 1407.6057

    Article  Google Scholar 

  144. Heinz U, Snellings R (2013) Collective flow and viscosity in relativistic heavy-ion collisions. Ann Rev Nucl Part Sci 63:123–151. arXiv:1301.2826

  145. Bernhard JE, Scott Moreland J, Bass SA, Liu J, U Hei (2016)z. Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium. Phys Rev C 94(2):024907. arXiv:1605.03954

  146. Everett D et al (2020) Multi-system Bayesian constraints on the transport coefficients of QCD matter. 11. arXiv:2011.01430

  147. Nijs G, van der Schee W, Gürsoy U, Snellings R (2020) A transverse momentum differential global analysis of heavy ion collisions. 10. arXiv:2010.15130

  148. Jia J, Zhang C, Xu J (2020) Centrality fluctuations and decorrelations in heavy-ion collisions in a Glauber model. Phys Rev Res 2(2):023319. arXiv:2001.08602

  149. Schnedermann E, Sollfrank J, Heinz UW (1993) Thermal phenomenology of hadrons from 200A GeV S+S collisions. Phys Rev C 48:2462

    Article  Google Scholar 

  150. Adamczyk L et al (2020) Bulk properties of the system formed in Au+Au collisions at \(\sqrt{s_{\rm NN}}= 14.5\,{\rm GeV}\). Phys Rev C 101(2):024905. arXiv:1908.03585

  151. Abelev B et al (2013) Centrality dependence of \(\pi \), K, p production in Pb-Pb collisions at \(\sqrt{s_{NN}}\) = 2.76 TeV. Phys Rev C 88:044910. arXiv:1303.0737

  152. Adamczyk L et al (2014) Beam-energy dependence of the directed flow of protons, antiprotons, and pions in Au+Au collisions. Phys Rev Lett 112(16):162301 1401.3043

    Article  Google Scholar 

  153. Adamczyk L et al (2018) Beam-energy dependence of directed flow of \(\Lambda \), \(\bar{\Lambda }\), \(K^\pm \), \(K^0_s\) and \(\phi \) in Au+Au collisions. Phys Rev Lett 120(6):062301. arXiv:1708.07132

  154. Heinz UW (2010) Relativistic heavy ion physics. Landolt- Bornstein data collection series, vol 23(I)

    Google Scholar 

  155. Bass SA et al (1998) Microscopic models for ultrarelativistic heavy ion collisions. Prog Part Nucl Phys 41:255

    Article  Google Scholar 

  156. Bleicher M et al (1999) Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model (UrQMD). J Phys G 25:1859

    Article  Google Scholar 

  157. Rischke D et al (1996) The phase transition to the quark-gluon plasma and its effect on hydrodynamic flow. Heavy Ion Phys 1:209

    Google Scholar 

  158. Stocker H (2005) Collective flow signals the quark gluon plasma. Nucl Phys A 750:121

    Article  Google Scholar 

  159. Steinheimer J, Auvinen J, Petersen H, Bleicher M, Stöcker H (2014) Examination of directed flow as a signal for a phase transition in relativistic nuclear collisions. Phys Rev C 89(5):054913 1402.7236

    Article  Google Scholar 

  160. Nayak K et al (2019) Energy dependence study of directed flow in Au+Au collisions using an improved coalescence in a multiphase transport model. Phys Rev C 100:054903

    Article  Google Scholar 

  161. Reisdorf W et al (2012) Systematics of azimuthal asymmetries in heavy ion collisions in the 1 A GeV regime. Nucl Phys A 876:1–60. arXiv:1112.3180

  162. Pinkenburg C et al (1999) elliptic flow: transition from out-of-plane to in-plane emission in Au+Au collisions. Phys Rev Lett 83:1295

    Article  Google Scholar 

  163. Alt C et al (2003) Directed and elliptic flow of charged pions and protons in Pb+Pb collisions at 40A and 158A GeV. Phys Rev C 68:034903

    Article  Google Scholar 

  164. Andronic A et al (2005) Excitation function of elliptic flow in Au + Au collisions and the nuclear matter equation of state. Phys Lett B 612:173

    Article  Google Scholar 

  165. Braun-Munzinger P, Stachel J (1998) Dynamics of ultra-relativistic nuclear collisions with heavy beams: an experimental overview. Nucl Phys A 638:3c

    Article  Google Scholar 

  166. Appelshauser H (2002) New results from CERES. Nucl Phys A 698:253c

    Article  Google Scholar 

  167. Aamodt K et al (2010) Elliptic flow of charged particles in Pb+Pb collisions at \(\sqrt{s_{NN}}\) = 2.76 TeV. Phys Rev Lett 105:252302

    Google Scholar 

  168. Voloshin SA, Poskanzer AM, Snellings R (2010) Collective phenomena in non-central nuclear collisions. Relativistic heavy ion. Springer, Berlin/Heidelberg, Germany, pp 293–333

    Google Scholar 

  169. Adams J et al (2005) Azimuthal anisotropy in Au+Au collisions at \(\sqrt{s_{NN}}\) = 200 GeV. Phys Rev C 72:014904

    Article  Google Scholar 

  170. Adler C et al (2002) Elliptic flow from two- and four-particle correlations in Au+Au collisions at \(\sqrt{s_{NN}}\) = 130 GeV. Phys Rev C 66:034904

    Article  Google Scholar 

  171. Adare A et al (2007) Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at \(\sqrt{s_{NN}}\) = 200 GeV. Phys Rev Lett 98:162301

    Article  Google Scholar 

  172. Alver B et al (2007) System size, energy, pseudorapidity, and centrality dependence of elliptic flow. Phys Rev Lett 98:242302

    Article  Google Scholar 

  173. Adamczyk L et al (2012) Inclusive charged hadron elliptic flow in Au+Au collisions at \(\sqrt{s_{NN}}\) = 7.7–39 GeV. Phys Rev C 86:054908

    Google Scholar 

  174. Shi S (2013) Event anisotropy \(v_2\) in Au+Au collisions at \(\sqrt{s_{NN}}\) = 7.7–62.4 GeV with STAR. Nucl Phys A 904-905:895c

    Google Scholar 

  175. Adamczyk L et al (2013) Observation of an energy-dependent difference in elliptic flow between particles and antiparticles in relativistic heavy ion collisions. Phys Rev Lett 110:142301

    Article  Google Scholar 

  176. Adamczyk L et al (2013) Elliptic flow of identified hadrons in Au + Au collisions at \(\sqrt{s_{NN}}\) = 7.7–62.4 GeV. Phys Rev C 88:014902

    Google Scholar 

  177. Adamczyk L et al (2016) Centrality dependence of identified particle elliptic flow in relativistic heavy-ion collisions at \(\sqrt{s_{NN}}\) = 7.7–62.4 GeV. Phys Rev C 93:014907

    Google Scholar 

  178. Kolb PF, Sollfrank J, Heinz U (2000) Anisotropic transverse flow and the quark-hadron phase transition. Phys Rev C 62:054909

    Article  Google Scholar 

  179. Sorge H (1999) Highly sensitive centrality dependence of elliptic flow: a novel signature of the phase transition in QCD. Phys Rev Lett 82:2048

    Article  Google Scholar 

  180. Auvinen J, Petersen H (2013) Evolution of elliptic and triangular flow as a function of \(\sqrt{{s}_{NN}}\) in a hybrid model. Phys Rev C 88(6):064908 1310.1764

    Article  Google Scholar 

  181. Petersen H, Bleicher M (2010) Eccentricity fluctuations in an integrated hybrid approach: Influence on elliptic flow. Phys Rev C 81:044906. arXiv:1002.1003

  182. Steinheimer J, Koch V, Bleicher M (2012) Hydrodynamics at large baryon densities: understanding proton versus anti-proton \(v_2\) and other puzzles. Phys Rev C 86:044903

    Article  Google Scholar 

  183. Hatta Y, Monnai A, Xiao B-W (2015) Flow harmonics \(v_n\) at finite density. Phys Rev D 92:114010

    Article  Google Scholar 

  184. Xu J, Song T, Ko C, Li F (2014) Elliptic flow splitting as a probe of the QCD phase structure at finite baryon chemical potential. Phys Rev Lett 112:012301

    Article  Google Scholar 

  185. Liu H et al (2019) Isospin splitting of pion elliptic flow in relativistic heavy-ion collisions. Phys Lett B 798:135002

    Article  Google Scholar 

  186. Tu B, Shi S, Liu F (2019) Elliptic flow of transported and produced protons in Au+Au collisions with the UrQMD model. Chin Phys C 43:054106

    Article  Google Scholar 

  187. Adamczyk L et al (2016) Centrality and transverse momentum dependence of elliptic flow of multistrange hadrons and \(\phi \) Meson in Au + Au collisions at \(\sqrt{s_{NN}}\) = 200 GeV. Phys Rev Lett 116:062301

    Article  Google Scholar 

  188. Adamczyk L et al (2017) Measurement of \(D^0\) azimuthal anisotropy at midrapidity in Au + Au collisions at \(\sqrt{s_{NN}}\) = 200 GeV. Phys Rev Lett 118:212301

    Article  Google Scholar 

  189. Luo X, Shi S, Xu N, Zhang Y (2020) A study of the properties of the QCD phase diagram in high-energy nuclear collisions. Particles 3(2):278–307. arXiv:2004.00789

  190. Shi S (2016) An experimental review on elliptic flow of strange and multistrange hadrons in relativistic heavy ion collisions. Adv High Energy Phys 2016:1987432. arXiv:1607.04863

  191. Bezverkhny Abelev B et al (2015) Elliptic flow of identified hadrons in Pb-Pb collisions at \( \sqrt{s_{\rm NN}}=2.76 \) TeV. JHEP 06:190. arXiv:1405.4632

  192. Abdallah M et al (2021) Disappearance of partonic collectivity in \(\sqrt{s_{NN}}\) = 3 GeV Au+Au collisions at RHIC. 8. arXiv: 2108.00908

  193. Dong X, Esumi S, Sorensen P, Xu N, Xu Z (2004) Resonance decay effects on anisotropy parameters. Phys Lett B 597:328–332. arXiv: nucl-th/0403030

  194. Adam J et al (2020) Flow and interferometry results from Au+Au collisions at \(\sqrt{s_{NN}} = 4.5\) GeV. 7. arXiv:2007.14005

  195. Snellings R et al (2000) Novel rapidity dependence of directed flow in high-energy heavy ion collisions. Phys Rev Lett 84:2803–2805 nucl-ex/9908001

    Article  Google Scholar 

  196. Abdallah M et al (2021) Light nuclei collectivity from \(\sqrt{s_{\rm NN}}\) = 3 GeV Au+Au collisions at RHIC. 12. arXiv:2112.04066

  197. Adamczyk L et al (2016) Measurement of elliptic flow of light nuclei at \(\sqrt{s_{NN}}=\) 200, 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV at the BNL relativistic heavy ion collider. Phys Rev C 94(3):034908. arXiv:1601.07052

  198. Adamczewski-Musch J et al (2020) Directed, elliptic, and higher order flow harmonics of protons, deuterons, and tritons in \(\rm Au\mathit{+\rm Au}\) collisions at \(\sqrt{{s}_{NN}}=2.4 \rm GeV\). Phys Rev Lett 125:262301. arXiv:2005.12217

  199. Alver B, Roland G (2010) Collision geometry fluctuations and triangular flow in heavy-ion collisions. Phys Rev C 81:054905. arXiv: 1003.0194. [Erratum: Phys. Rev. C 82, 039903 (2010)]

  200. Aad G et al (2012) Measurement of the azimuthal anisotropy for charged particle production in \(\sqrt{s_{NN}}=2.76\) TeV lead-lead collisions with the ATLAS detector. Phys Rev C 86:014907. arXiv: 1203.3087

  201. Aad G et al (2014) Measurement of event-plane correlations in \(\sqrt{s_{NN}}=2.76\) TeV lead-lead collisions with the ATLAS detector. Phys Rev C 90(2):024905. arXiv:1403.0489

  202. Adam J et al (2016) Correlated event-by-event fluctuations of flow harmonics in Pb-Pb collisions at \(\sqrt{s_{_{\rm NN}}}=2.76\) TeV. Phys Rev Lett 117:182301. arXiv:1604.07663

  203. Aad G et al (2014) Measurement of long-range pseudorapidity correlations and azimuthal harmonics in \(\sqrt{s_{NN}}=5.02\) TeV proton-lead collisions with the ATLAS detector. Phys Rev C 90(4):044906. arXiv:1409.1792

  204. Jia J, Zhou M, Trzupek A (2017) Revealing long-range multiparticle collectivity in small collision systems via subevent cumulants. Phys Rev C 96(3):034906. arXiv:1701.03830

  205. Huo P, Gajdošová K, Jia J, Zhou Y (2018) Importance of non-flow in mixed-harmonic multi-particle correlations in small collision systems. Phys Lett B 777:201–206. arXiv:1710.07567

  206. Zhang C, Jia J, Xu J (2019) Non-flow effects in three-particle mixed-harmonic azimuthal correlations in small collision systems. Phys Lett B 792:138–141. arXiv:1812.03536

  207. Alver B et al (2008) Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions. Phys Rev C 77:014906. arXiv:0711.3724

  208. Aaboud M et al (2018) Measurement of long-range multiparticle azimuthal correlations with the subevent cumulant method in \(pp\) and \(p + Pb\) collisions with the ATLAS detector at the CERN Large Hadron Collider. Phys Rev C 97(2):024904. arXiv:1708.03559

  209. Aad G et al (2013) Measurement of the distributions of event-by-event flow harmonics in lead-lead collisions at = 2.76 TeV with the ATLAS detector at the LHC. JHEP, 11:183. arXiv:1305.2942

  210. Chatrchyan S et al (2014) Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at \(\sqrt{s_{NN}}\) = 2.76 TeV. Phys Rev C 89(4):044906. arXiv:1310.8651

  211. Yan L (2018) A flow paradigm in heavy-ion collisions. Chin Phys C 42(4):042001. arXiv:1712.04580

  212. Yan L, Grönqvist H (2016) Hydrodynamical noise and Gubser flow. JHEP 03:121. arXiv: 1511.07198

  213. Sakai A, Murase K, Hirano T (2020) Rapidity decorrelation of anisotropic flow caused by hydrodynamic fluctuations. Phys Rev C 102(6):064903. arXiv:2003.13496

  214. Schenke B, Shen C, Tribedy P (2020) Running the gamut of high energy nuclear collisions. Phys Rev C 102(4):044905. arXiv:2005.14682

  215. Hillmann P, Steinheimer J, Bleicher M (2018) Directed, elliptic and triangular flow of protons in Au+Au reactions at 1.23 A GeV: a theoretical analysis of the recent HADES data. J Phys G 45(8):085101. arXiv:1802.01951

  216. Giacalone G, Gardim FG, Noronha-Hostler J, Ollitrault J-Y (2021) Skewness of mean transverse momentum fluctuations in heavy-ion collisions. Phys Rev C 103(2):024910. arXiv:2004.09799

  217. Bozek P (2016) Transverse-momentum–flow correlations in relativistic heavy-ion collisions. Phys Rev C 93(4):044908. arXiv:1601.04513

  218. Jia J, Huo P (2014) Forward-backward eccentricity and participant-plane angle fluctuations and their influences on longitudinal dynamics of collective flow. Phys Rev C 90(3):034915 1403.6077

    Article  Google Scholar 

  219. Shou QY, Ma YG, Sorensen P, Tang AH, Videbæk F, Wang H (2015) Parameterization of deformed nuclei for glauber modeling in relativistic heavy ion collisions. Phys Lett B 749:215–220. arXiv:1409.8375

  220. Giacalone G (2020) Observing the deformation of nuclei with relativistic nuclear collisions. Phys Rev Lett 124(20):202301. arXiv:1910.04673

  221. Xu H-j, Li H, Wang X, Shen C, Wang F (2021) Determine the neutron skin type by relativistic isobaric collisions. Phys Lett B 819:136453. arXiv:2103.05595

  222. Jia J (2022) Shape of atomic nuclei in heavy ion collisions. Phys Rev C 105(1):014905. arXiv:2106.08768

  223. Jia J (2022) Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions. Phys Rev C 105(4):044905. arXiv:2109.00604

  224. Zhang C, Jia J (2022) Evidence of quadrupole and octupole deformations in \(^{96}\)Zr+\(^{96}\)Zr and \(^{96}\)Ru+\(^{96}\)Ru collisions at ultra-relativistic energies. Phys Rev Lett 128(2):022301. arXiv:2109.01631

Download references

Acknowledgements

This work is partly supported by the Chinese National Natural Science Foundation under Grant Nos: 11861131009 and 12075098, and in part by the National Science Foundation (NSF) under grant numbers PHY-2012922 and PHY-2012947 (Z.W.L.), and by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under contract numbers DE-SC001346 and DE-SC0021969, and within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration, and Grants-in-Aid for Scientific Research from JSPS (JP21K03577). J.Y. Jia research is supported in part by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under contract number DEFG0287ER40331, and by the National Science Foundation (NSF) under grant number PHY-1913138. Y. Y. would like to acknowledge financial support from the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB34000000. M. Stephanov is supported by D.O.E with grant No. DE-FG0201ER41195. S.S. Shi would like to acknowledge financial support from the National Natural Science Foundation of China under Grant Nos. 11890710(11890711) and 12175084 and the National Key Research and Development Program of China under Grant No. 2020YFE0202002. L.Y. is supported in part by the National Natural Science Foundation of China under grant number 11975079.

Author information

Authors and Affiliations

  1. Akita International University, Yuwa, Akita-city, 010-1292, Japan

    Y. Nara

  2. Department of Chemistry, Stony Brook University, Stony Brook, NY, 11794, USA

    J. Y. Jia

  3. Brookhaven National Laboratory, Upton, NY, 11973, USA

    J. Y. Jia & C. Shen

  4. Wayne State University, Detroit, Michigan, 48201, USA

    C. Shen

  5. Central China Normal University, Wuhan, China

    L. G. Pang & S. S. Shi

  6. East Carolina University, Greenville, NC, 27858, USA

    Z. W. Lin

  7. GSI Helmholtzzentrum für Schwerionenforschung, Planckstr. 1, 64291, Darmstadt, Germany

    H. Elfner

  8. Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438, Frankfurt am Main, Germany

    H. Elfner

  9. Goethe University, Max-von-Laue-Strasse 1, 60438, Frankfurt am Main, Germany

    H. Elfner

  10. Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtz Center, Campus Frankfurt, Max-von-Laue-Strasse 12, 60438, Frankfurt am Main, Germany

    H. Elfner

  11. Fudan University, Shanghai, 200433, China

    L. Yan

  12. Institute of Modern Physics, Chinese Academy of Sciences, Gansu, 730000, China

    Y. Yin

  13. Tsinghua University, Beijing, 100084, China

    P. F. Zhuang

  14. University of Illinois at Chicago, Chicago, IL, 60607, USA

    M. Stephanov

Authors
  1. H. Elfner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Y. Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. W. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Nara
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. G. Pang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. S. S. Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. M. Stephanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. L. Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Y. Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. P. F. Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. F. Zhuang .

Editor information

Editors and Affiliations

  1. College of Physical Science and Technology, Central China Normal University, Wuhan, China

    Xiaofeng Luo

  2. Department of Modern Physics, University of Science and Technology of China, Hefei, China

    Qun Wang

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Nu Xu

  4. Department of Physics, Tsinghua University, Beijing, China

    Pengfei Zhuang

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Science Press

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Elfner, H. et al. (2022). Dynamical Evolution of Heavy-Ion Collisions. In: Luo, X., Wang, Q., Xu, N., Zhuang, P. (eds) Properties of QCD Matter at High Baryon Density. Springer, Singapore. https://doi.org/10.1007/978-981-19-4441-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-19-4441-3_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-4440-6

  • Online ISBN: 978-981-19-4441-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation