Effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter

Abstract

We have studied the effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter by estimating their respective response functions, such as the electrical conductivity ($σ_{\rm el}$), the Hall conductivity ($σ_{\rm H}$), the thermal conductivity ($κ_0$) and the Hall-type thermal conductivity ($κ_1$). The expressions of charge and heat transport coefficients are obtained by solving the relativistic Boltzmann transport equation in the relaxation time approximation at weak magnetic field and finite chemical potential. The interactions among partons are incorporated through their thermal masses. We have observed that $σ_{\rm el}$ and $κ_0$ decrease and $σ_{\rm H}$ and $κ_1$ increase with the magnetic field in the weak magnetic field regime. On the other hand, the presence of a finite chemical potential increases these transport coefficients. The effects of weak magnetic field and finite chemical potential on aforesaid transport coefficients are found to be more conspicuous at low temperatures, whereas at high temperatures, they have only a mild dependence on magnetic field and chemical potential. We have found that the presence of finite chemical potential further extends the lifetime of the magnetic field. Furthermore, we have explored the effects of weak magnetic field and finite chemical potential on the Knudsen number, the elliptic flow coefficient and the Wiedemann-Franz law.