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Chiral Anomaly and Local Polarization Effect from Quantum Transport Approach

Chiral Anomaly and Local Polarization Effect from Quantum Transport Approach. 高建华 山东大学（威海）. J.H. Gao , Z.T. Liang, S. Pu , Q. Wang, X.N. Wang, PRL 109, 232301(2012). 中国物理学会高能物理分会第九届全国会员代表大会暨学术年会 2014 年 4 月 18 ～ 23 日 武汉. Outline. Introduction Chiral Anomalous Fluid

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Chiral Anomaly and Local Polarization Effect from Quantum Transport Approach

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  1. Chiral Anomaly and Local Polarization Effect from Quantum Transport Approach 高建华 山东大学（威海） J.H. Gao, Z.T. Liang, S. Pu, Q. Wang, X.N. Wang, PRL 109, 232301(2012) 中国物理学会高能物理分会第九届全国会员代表大会暨学术年会2014年4月18～23日 武汉

  2. Outline • Introduction • Chiral Anomalous Fluid • Chiral Anomalous Fluid from Quantum Transport Approach • Summary

  3. Quantum Chromo Dynamics QCD : Quark Confinement: Chiral Symmetry breaking: Asymptotic freedom:

  4. Instanton and Sphaleron Gluon field configuration with topological winding number: Lepton and baryon number non-conservation Strong CPviolation

  5. Anomalous fluid in HIC Hydrodynamics with EM fields: Sphaleron Chirality imbalance: Chiral current: Hydrodynamic equations with anomalousaxial current :

  6. Hydrodynamics with Chiral Anomalies Hydrodynamic Equation with Anomalies : D.T. Son, P. SurowkaPRL103:191601,2009 Requiring, The new kinetic coefficients can be fixed uniquely:

  7. Hydrodynamics with Chiral Anomalies From one current to two currents: S. Pu, J.H. Gao, Q. W. PRD83:094017,2011 Requiring

  8. CME & CVE Chiral magnetic effect Chiralvortical effect K.Fukushma, D.E.Kharzeev, H.J.Warringa PRD78:074033,2008 + _ (A+A 200GeV) STAR collaboration PRL 103 (2009) 251601

  9. From Macroscopic to Microscopic Classical transport approach Probability density function Quantum transport approach Wigner functions The ensemble average of Wigner operator: Gauge invariant Wigner operator: Gauge link D.Vasak, M.Gyulassy, H. Elze Annals Phys. 173 (1987) 462-492

  10. Quantum Transport Equations Wigner equations for masslesscollisionless particle system in homogeneous background EM field : Wigner functions can be expanded as : Vector parts: Scalar and tensor parts:

  11. Perturbative Expansion Scheme In order to find the solutions near the equilibrium, we can expand and in powers of and 0-th order: 1-st order: One more operator One more order Iterative equations: The equations can be solved in a very consistent iterative scheme !

  12. The 0-th Order Solution The 0-th order equations: The 0-th order solutions take the local equilibrium form: :Local flow 4-velocity

  13. The 1-st Order Solution Constraint conditions for Vlasovequation Evolution equations for ideal fluids Consider the local static solutions The first order solution can be generally made from Iterative equations:

  14. Chiral Anomaly Integrate over the momentum All the conservation laws and anomaly can be derived naturally:

  15. CME , CVE, LPE CME: CVE: Reversal chiral magnetic effect Local polarization effect LPE should be present in both high and low energy heavy-ion collisions with either low baryonic chemical potential and high temperature or vice versa.

  16. Approaches to CME/CVE • Gauge/Gravity Duality • Erdmenger et.al., JHEP 0901,055(2009); Banerjee, et.al., JHEP 1101,094(2011); • Torabian and Yee, JHEP 0908,020(2009); Rebhan, Schmitt and Stricher, JHEP1001,026(2010); • Kalaydzhyan and Kirsch, et.al, PRL 106,211601(2011) …… • Hydrodynamics with Entropy Principle • Son and Surowka, PRL 103,191601(2009); Kharzeev and Yee, PRD 84,045025(2011); • Pu,Gao and Wang, PRD 83,094017(2011)…… • Quantum Field Theory • Metlitski and Zhitnitsky, PRD 72,045011(2005); Newman and Son, PRD 73, 045006(2006); • Lublinsky and Zahed, PLB 684,119(2010); Asakawa, Majumder and Muller, PRC81, • 064912(2010);Landsteiner,Megias and Pena-Benitez, PRL 107,021601(2011); • Hou, Liu and Ren, JHEP 1105,046(2011); Hou, Liu and RenPRD86(2012)121703…… • Quantum Kinetic Approach • Stephanov and Yin PRL 109,(2012)162001, Son and Yamamoto PRD 87 (2013) 8, 085016; • Chen, Pu, Q.Wang and X.N. Wang, PRL 110 (2013)262301

  17. Summary • A consistent iterative scheme to solve quantum transport equations has been set up, in which transport approach, hydro expansion and chiral anomaly are totally consistent with each other. • Induced currents by vorticity and magnetic field are natural results of quantum transport theory. • A local polarization effect due to the vorticity can be expected in non-central heavy ion collisions. • The success of this approach urges us to go further: First order Second order, … Constant EM field Arbitrary EM field Non-interacting system Interacting system, QGP

  18. 谢谢！

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