Effects Of Magnetic Field And Vorticity In Relativistic Heavy-ion Collisions

Relativistic heavy-ion collisions can generate quark-gluon plasma(QGP),as well as strong electromagnetic fields and fluid vorticities.These strong fields can lead to anomalous transport phenomena such as the Chiral Magnetic Effect(CME)and the Chiral Vortical Effect(CVE).They refer to respectively the vector flows induced by the magnetic field and the vorticity field along their directions.In heavy-ion collisions,it is expected that they lead to the charge separation effect and baryon separation effect,respectively.Current experimental results qualitatively support the expectation of these effects,but there is a large background to the observables which can not be removed from the signal.On the theory side,in order to give predictions of these effects quan-titatively,it is necessary to describe in accuracy the space-time evolution of magnetic fields and vorticities in heavy-ion collisions.The first part of this thesis is to study the magnetic field in conducting medium with the chiral conductivity.We start from the magnetic field distribution at the initial moment of heavy-ion collisions.At this moment,two atomic nuclei moving at a high speed will produce an extremely large magnetic field.In vacuum,this magnetic field decays rapidly with time.In the real situation,the QGP matter has Ohmic conductivity,so the induced current can delay the attenuation of the magnetic field.We also consider the influence of the chiral magnetic effect on the evolution of the magnetic field.The evolution of the magnetic field with the chiral magnetic effect can be described by the anomalous Maxwell equations.We solve these equations by expanding the magnetic field in vector spherical harmonics.Our results clearly show that there is a growth mode in the evolution of the magnetic field over time.This is because the magnetic field induces a current along its direction from the CME,which in turn generates a magnetic field.This positive feedback mode causes the magnetic field to have an increasing mode.In a physical system,the fermion's helicity and the magnetic field's helicity can be transformed into each other.When the growth mode of the magnetic field appears,it decreases the difference in the number of fermions between the right-handed and the left-handed,and then suppresses the chiral conductivity and the growth rate of the magnetic field.Both the asymptotic solution of the magnetic field and the numerical calculation show that in the system where the total helicity is conserved,the growth mode of the magnetic field is finally suppressed before causing the divergence.In the second part,we study the spatial structure of the vorticity field in QGP.Vorticity reflects the local rotation of the fluid field.It can arise from the shear flow caused by the initial orbital angular momentum in non-central collisions,or from the non-uniform expansion of the fireball,including the anisotropy of the transverse flow in the transverse plane such as the elliptic flow,and the dependence of the transverse flow on the longitudinal coordinate.The vorticity fields from different sources have different spatial structures:the one generated by the orbital angular momentum is per-pendicular to the reaction plane on average;while the one generated by the non-uniform expansion of the fireball is in different directions in different region,which shows a ring or quadrupole structure.In heavy-ion collisions,the ? polarization can be used as a probe to the space-time information of the vorticity field in the fireball.We sim-ulated the collective evolution of the fireball by the AMPT model and calculated the polarization of the vorticity field and the A polarization.In our results,the global A polarization associated with the orbital angular momentum is in agreement with the existing experimental measurements.We also calculated the local A polarization asso-ciated with the non-uniform expansion of the fireball and hope it can be measured in future experiments.