# Effect of time-varying electromagnetic field on Wiedemann-Franz law in a hot hadronic matter

## TL;DR

This paper investigates how time-varying magnetic fields influence electrical and thermal conductivities in hadron resonance gas, revealing deviations from the Wiedemann-Franz law at different temperatures and magnetic field conditions.

## Contribution

It introduces a kinetic theory approach to quantify the effects of time-varying magnetic fields on conductivities and the Wiedemann-Franz law in hadronic matter, a novel analysis in this context.

## Key findings

- Conductivities depend on relaxation and decay times in a time-varying magnetic field.
- The Wiedemann-Franz law shows saturation at high temperatures with quantifiable deviations at low temperatures.
- First quantitative analysis of Wiedemann-Franz law deviations in hadron resonance gas under dynamic magnetic fields.

## Abstract

We have estimated the electrical and thermal conductivity of a hadron resonance gas 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 and thermal conductivity in terms of relaxation and decay times. In the absence of the magnetic field, only a single time scale appears, and in the finite magnetic field case, their expressions carry two-time scales, 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.