Magnetoviscosity of relativistic plasma

TL;DR

This work develops a first-principles quantum-field-theory framework to compute the magnetoviscosity of relativistic plasmas under strong magnetic fields using Kubo relations and a Landau-level spectral representation. By incorporating Landau-level damping rates $\Gamma_n(k_z)$ from leading $1\leftrightarrow 2$ processes, it derives analytic expressions for the transverse and longitudinal shear viscosities $\eta_{\perp}$ and $\eta_{\parallel}$, as well as the transverse and longitudinal bulk viscosities $\zeta_{\perp}$, $\zeta_{\parallel}$, and the cross viscosity $\zeta_{\times}$, with precise Landau-level transition rules (e.g., $\eta_{\parallel}$ couples adjacent levels $n\to n+1$ while $\eta_{\perp}$ also involves $n\to n+2$). In hot magnetized QED, the results show strong anisotropy: $\eta_{\parallel}/T^3$ rises rapidly with $|eB|/T^2$, while $\eta_{\perp}/T^3$ is suppressed and can fall below the KSS bound at large fields; bulk viscosities display nonmonotonic behavior and high sensitivity to the sound velocities, with $\zeta_{\times}$ negative and field-enhanced. Extending to QCD, qualitative trends persist in a strongly magnetized two-flavor plasma, though quantitative features depend on the coupling $\alpha_s$, indicating that magnetoviscosity remains a robust but coupling-sensitive diagnostic for heavy-ion and astrophysical environments. Overall, the paper provides a microscopic, Landau-level-resolved framework for magnetoviscosity with implications for magnetar dynamics and magnetized quark-gluon plasmas, and suggests avenues to implement these anisotropic transport coefficients in relativistic magnetohydrodynamics and related phenomenology.

Abstract

Using first-principles quantum field-theoretical methods, we investigate the shear and bulk viscosities of strongly magnetized relativistic plasmas. The analysis is performed within the weak-coupling approximation and utilizes known results for the fermion damping rates in the Landau-level representation, $Γ_{n}(p_{z})$, which are dominated by one-to-two and two-to-one processes in the presence of a strong magnetic field. The transverse and longitudinal components of the viscosities are derived using Kubo's linear response theory. Our results reveal a pronounced anisotropy in both shear and bulk viscosities induced by the magnetic field. In the case of an electron-positron plasma, where the weak-coupling approximation is well justified, the dimensionless longitudinal shear viscosity $η_{\parallel}/T^3$ increases rapidly with the magnetic field strength, while the transverse component $η_{\perp}/T^3$ decreases and can even drop below the KSS bound at sufficiently large fields. In contrast, both the dimensionless longitudinal and transverse bulk viscosities, $ζ_{\perp}/T^3$ and $ζ_{\parallel}/T^3$, initially rise from small values, reach a maximum, and then gradually decrease toward zero. We find that the bulk viscosity is highly sensitive to the longitudinal and transverse components of the sound velocity, particularly at high magnetic fields, indicating that its quantitative values should be interpreted with caution. We also calculate an additional cross viscosity, which is negative and whose magnitude increases with the magnetic field strength. Finally, we discuss the physical implications of these magnetoviscosity results in the contexts of magnetar physics and the strongly magnetized quark-gluon plasma produced in heavy-ion collisions.

Figures (5)

• 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 transverse and longitudinal components of the shear (left) and bulk (right) viscosities as functions of the dimensionless ratio $|eB|/T^2$ in a magnetized QED plasma. Empty markers and interpolating lines represent the results in the chiral limit. Filled markers represents the results for the massive case.
• Figure 3: Left panel: Transverse and longitudinal components of the speed of sound squared in strongly magnetized QED and QCD plasmas. Right panel: Transverse and longitudinal bulk viscosities in QED (solid lines), together with their variation range corresponding to $\pm 10^{-7}$ changes in $\delta v_{\perp}^2$ and $\delta v_{\parallel}^2$.
• Figure 4: The negative cross viscosity as a function of the dimensionless ratio $|eB|/T^2$ in a magnetized QED (left) and QCD (right) plasmas. Empty markers with interpolating lines correspond to results in the chiral limit, while filled markers represent the massive case.
• Figure 5: The transverse and longitudinal components of the shear (left) and bulk (right) viscosities as functions of the dimensionless ratio $|eB|/T^2$ in a magnetized QCD plasma for two representative values of the strong coupling constant, $\alpha_s = 0.5$ and $\alpha_s = 1$. Empty markers with interpolating lines correspond to results in the chiral limit, while filled markers represent the massive case.