磁化费米子系统中的电导率和磁导率
Electric and magnetic conductivities in magnetized fermion systems
AI总结：
本文在弛豫时间近似的Wigner函数方法下，解析和数值计算了强磁场中费米子系统的电导率和磁导率，给出了纵向、横向Ohm电导率及Hall电导率随时间的演化行为。
摘要：
在弛豫时间近似的Wigner函数方法中，我们计算了强磁场中费米子系统的电导率和磁导率。我们计算了电磁场对背景恒定磁场微扰的线性响应。Wigner函数被分为背景磁场中的平衡部分和由微扰场诱导的非平衡部分。给出了平衡部分的解析表达式以及相应的平衡条件。对于非平衡部分，我们从Wigner函数的主方程中得到了$\hbar$领头阶的动力学方程。当微扰场仅依赖于固有时时，非平衡部分可以解析求解，由此得到矢量流和轴矢量流。我们得到了纵向和横向Ohm电导率以及Hall电导率，作为矢量流对微扰电场的线性响应。我们解析和数值地研究了这些电导率随演化时间、弛豫时间、粒子质量和背景磁场强度的变化行为。
英文摘要：
In Wigner function approach with relaxation time approximation, we calculate electric and magnetic conductivities of a fermion system in the strong magnetic field. The linear response has been calculated to the perturbation of electromagnetic fields on the background constant magnetic field. The Wigner function is separated into an equilibrium part in the background magnetic field and an off-equilibrium part induced by perturbative fields. The analytical expression for the equilibrium part and the corresponding equilibrium conditions are given. For the off-equilibrium part, we obtain the kinetic equation at the leading order in $\hbar$ from the master equation of the Wigner function. When perturbative fields only depend on the proper time, the off-equilibrium part can be analytically solved from which the vector and axial vector currents are obtained. We obtain the longitudinal and transverse Ohm conductivities as well as Hall conductivity as the linear response of the vector current to the perturbative electric field. The behaviors of these conductivities as functions of the evolving time, relaxation time, particle mass, and strength of the background magnetic field are investigated both analytically and numerically.
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