| High energy heavy-ion collision is an essential tool to explore the origin of the universe and the fundamental structure of matter.The hot and dense matter generated in heavy-ion collisions,known as quark-gluon plasma(QGP),is a new state of strongly interacting matter and is also present in the early universe.In non-central collisions,there’re huge orbital angular momenta and strong magnetic fields,which have new physical effects.Due to spin-orbit coupling,such large orbital angular momenta can be partially transferred to the spin polarization of quark matter,resulting in spin polarization.Quark polarization will be converted to hadrons during hadronization,which can be finally detected in experiments.Spin polarization can be categorized as global spin polarization and local spin polarization.The current theory can explain global spin polarization well,but can not account for the sign puzzle of local spin polarization satisfactorily.In order to solve this problem,scientists have proposed many solutions,and spin fluid-dynamics is one of the solutions.The presence of a strong magnetic field can induce anomalous transport phenomena,such as CME,CSE and CMW.In addition,the magnetic field also affects various physical quantities,such as shear and bulk viscosities,diffusion constants and electrical conductivities.Among these physical quantities,the electrical conductivity is important,which directly affects the lifetime of the magnetic field and is also an indispensable parameter for magnetohydrodynamic simulation.We derive relativistic ideal spin hydrodynamics from the covariant Wigner function.Based on the covariant Wigner function in local thermal equilibrium,we derive hydrodynamical quantities of a spin-1/2 particle system:particle number density,energy momentum tensor,spin tensor and dipole moment tensor.Compared with ideal hydrodynamics without spin,we derive the first and second order terms in Knudsen number Kn and mean spin polarization χs.We derive the equations of motion of the first and second order thermodynamic parameters in Knudsen number Kn and mean spin polarization χs by the conservation law.The novelty of this work is the use of the local thermal equilibrium Wigner function to study relativistic ideal spin fluid and the calculation of the results to second order.We derive solutions for relativistic anomalous magnetohydrodynamics with longitudinal Bjorken invariance and transverse electromagnetic fields in the presence of temperature or energy density-dependent conductivity.We consider the equations of state in the high temperature limit or high chemical potential limit.Under the conditions of initial electromagnetic field and Bjorken velocity,we obtain the analytical and numerical solutions up to the order of h.Our results show that the conductivity related to temperature or energy density plays an important role in the attenuation of energy density and electromagnetic fields.We also apply our results to explain the splitting of global polarization for A and A hyperons caused by magnetic fields.The novelty of this work is the study of the anomalous magnetohydrodynamics with temperature-dependent conductivity,whereas previous works only considered constant conductivities.Finally,using the covariant Wigner function with relaxation time approximation,we study the linear response of a fermion system to the perturbative electromagnetic field under constant strong background magnetic field.The covariant Wigner function can be decomposed into two parts:the equilibrium part Weq in the background magnetic field and the non-equilibrium part δW induced by the perturbation field.We show the analytical solution of the equilibrium part and derive the associated equilibrium conditions.For the non-equilibrium part,we obtain the kinetic equation at the first order of h.When the perturbation field depends only on the proper part,the non-equilibrium part can be solved analytically.Meanwhile,we also derive vector current and axial vector current.The linear response of vector current to a perturbative electric field can be described in terms of longitudinal and transverse Ohm conductivity and Hall conductivity.The relationships of these conductivities with respect to evolution time,relaxation time,particle mass and background magnetic field strength are investigated both analytically and numerically.The novelty of this work is the first use of the covariant Wigner function with relaxation time approximation to study the linear response of a fermion system to perturbative electromagnetic fields in a constant strong background magnetic field. |
