Effect of time-varying electromagnetic field on Wiedemann-Franz law in a hot hadronic matter
Kamaljeet Singh, Jayanta Dey, R. Sahoo, Sabyasachi Ghosh
Abstract
We have estimated the electrical and thermal conductivity of a hadron resonance gas (HRG) for a time-varying magnetic field, which is also compared with constant and zero magnetic field cases. Considering the exponential decay of electromagnetic fields with time, a kinetic theory framework can provide the microscopic expression of electrical conductivity and thermal conductivity related to baryon current in terms of relaxation and decay times. In the absence of the magnetic field, only a single timescale appears, and in the finite magnetic field case, their expressions carry two timescales---relaxation time and cyclotron time period. Estimating the conductivities for HRG matter in three cases---zero, constant, and time-varying magnetic fields, we have studied the validity of the Wiedemann--Franz law. We noticed that at a high-temperature domain, the ratio saturates at a particular value, which may be considered as Lorenz number of the hadron resonance gas. With respect to the saturation values, the deviation of the Wiedemann--Franz law has been quantified at the low-temperature domain. For the first time, the present work sketches this quantitative deviation of the Wiedemann--Franz law for hadron resonance gas at a constant and a time-varying magnetic field.