The electrical and Hall conductivities in uniform magnetic field have been evaluated for an interacting pion gas using the kinetic theory approach within the ambit of relaxation time approximation (RTA). The in-medium cross sections vis a vis the relaxation time for $\pi \pi$ scattering were obtained using one-loop modified thermal propagator for the exchanged $\rho$ and $\sigma$ mesons using thermal field theoretic techniques. For higher values of the magnetic field a monotonical increase of the electrical conductivity with temperature was observed. However, for a given temperature the conductivity is found to decrease steadily with magnetic field. The Hall conductivity, at lower values of the magnetic field, was found to decrease with temperature more rapidly than the electrical conductivity, whereas at higher values of magnetic field, a linear increase was seen. Use of the in-medium scattering cross-section was found to produce a significant effect on the temperature dependence of both electrical and Hall conductivities compared to the case where vacuum cross-section was used.

中文翻译：

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对热的和磁化的介子气的电导率和霍尔电导率有中等影响

已经使用弛豫时间近似（RTA）范围内的动力学理论方法对相互作用的离子气体在均匀磁场中的电导率和霍尔电导率进行了评估。中间横截面相对于松弛时间$\pi \pi$ 使用单回路改进型传热器进行交换得到散射 $\rho$ 和 $\sigma$介子使用热场理论技术。对于更高的磁场值，观察到电导率随温度单调增加。然而，对于给定的温度，发现电导率随着磁场而稳定降低。发现在较低的磁场值下，霍尔电导率随温度的下降比电导率下降得更快，而在较高的磁场值下，则可见线性增长。与使用真空横截面的情况相比，发现使用介质中散射横截面对电导率和霍尔电导率的温度依赖性产生显着影响。