Review of heat and charge transport in strongly magnetized relativistic plasmas

TL;DR

This work addresses heat and charge transport in hot relativistic plasmas under strong magnetic fields by combining Kubo formalism with Landau-level spectral functions to compute anisotropic conductivities. The authors derive exact leading-order fermion damping rates $\Gamma_n(k_z)$ from inelastic one-to-two and two-to-one processes and use these as Lorentzian widths in spectral functions to obtain $\sigma_{\perp},\sigma_{\parallel},\kappa_{\perp},\kappa_{\parallel}$, revealing strong suppression of transverse transport and enhancement of longitudinal transport in the strong-field regime. Extending the framework from QED to QGP, they incorporate color and flavor factors and discuss the role of gluon damping, finding qualitative scaling with $|eB|/T^2$ but limited quantitative agreement with lattice QCD due to the leading-order approach; this underscores the need for higher-order and nonperturbative contributions. The study also shows a breakdown of the Wiedemann–Franz law in magnetized relativistic plasmas, with flavor-specific universal longitudinal Lorenz numbers emerging in the chiral limit $m\to0$, while transverse Lorenz numbers grow with $|eB|/T^2$, reflecting the distinct underlying transport mechanisms. Overall, the work provides a first-principles, anisotropic transport picture relevant for neutron stars, magnetars, and heavy-ion collisions, and points to future work incorporating subleading scatterings and nonperturbative effects to improve quantitative reliability.

Abstract

We review field-theoretic studies of charge transport in hot relativistic plasmas under strong magnetic fields and extend the analysis to thermal conductivity. The calculations rely on accurately determining the fermion damping rate. Using the Landau-level representation, these damping rates are computed exactly at leading order and incorporated into the Kubo formula to obtain the thermal and electrical conductivity tensors. Our analysis reveals that the mechanisms underlying longitudinal and transverse transport differ significantly. Strong magnetic fields markedly suppress transverse charge transport by confining particles within localized Landau orbits, allowing transport only through quantum transitions between these discrete states. In contrast, longitudinal charge transport is enhanced, as it primarily depends on the reduced scattering probability of particles moving along the direction of the magnetic field. The anisotropy of thermal conductivity is also nontrivial but less pronounced since its underlying transport mechanism is different. We also examine the modification of the Wiedemann--Franz law in strongly magnetized plasmas.

Figures (4)

• Figure 1: Leading order processes contributing to the fermion damping rates: (a) $\psi_{n}\to \psi_{n^\prime}+\gamma$ with $n >n^{\prime}$, (b) $\psi_{n}+\gamma\to\psi_{n^{\prime}}$ with $n<n^{\prime}$, (c) $\psi_{n}+\bar{\psi}_{n^{\prime}}\to\gamma$, where $n$ and $n^{\prime}$ are the Landau-level indices.
• Figure 2: The thermal (left) and electrical (right) conductivities as functions of the dimensionless ratio $|eB|/T^2$. Empty circles and interpolating dashed lines represent the results in the chiral limit.
• Figure 3: The thermal (left) and electrical (right) conductivities of two-flavor QGP as functions of the dimensionless ratio $|eB|/T^2$. Empty circles and interpolating dashed lines represent the results in the chiral limit.
• Figure 4: The transverse and longitudinal Lorenz numbers as functions of the dimensionless parameter $|eB|/T^2$ for QED plasma (left) and QGP (right). Results in the chiral limit are shown by empty circles and interpolating dashed lines. In the case of QGP (right), the results for two different choices of the coupling constant, $\alpha_s=0.5$ and $\alpha_s=1$, are shown.