Chirality dependence in charge and heat transport in thermal QCD

In the presence of weak magnetic field ($B$), novel phenomena, similar to Hall effect in condensed matter physics, emerge both in charge and heat transport in a thermal QCD medium. Here, we have employed the kinetic theory approach within a quasiparticle framework, wherein the effective masses for left (L) and right-handed (R) chiral modes of quarks are seen different, lifting the prevalent degeneracy. Another implication of weak $B$ is that the coefficients assume a tensorial structure: The diagonal elements represent the usual conductivities: $\sigma_{\text{Ohmic}}$ and $\kappa_0$ as the coefficients of charge and heat transport, respectively and the off-diagonal elements denote their Hall counterparts: $\sigma_{\text{Hall}}$ and $\kappa_1$, respectively. Finally, we have derived some coefficients, namely, the Knudsen number and Lorenz number in Wiedemann-Franz law. Lorenz number and Hall-Lorenz number for L-mode increases and for R-mode decreases with a magnetic field. it does not remain constant with $T$ hence violating the Wiedemann-Franz law.