Charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics

Abstract

We study charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics. In this theory, charge diffusion is not simply given by the standard Navier-Stokes form of Ohm's law, but by an evolution equation which ensures causality and stability. This, in turn, leads to transient effects in the charge diffusion current, the nature of which depends on the particular values of the electrical conductivity and the charge-diffusion relaxation time. The ensuing equations of motion are of so-called stiff character, which requires special care when solving them numerically. To this end, we specifically develop an implicit-explicit Runge-Kutta method for solving relativistic resistive second-order dissipative magnetohydrodynamics and subject it to various tests. We then study the system's evolution in a simplified 1+1-dimensional scenario for a heavy-ion collision, where matter and electromagnetic fields are assumed to be transversely homogeneous, and investigate the cases of an initially non-expanding fluid and a fluid initially expanding according to a Bjorken scaling flow. In the latter case, the scale invariance is broken by the ensuing self-consistent dynamics of matter and electromagnetic fields. However, the breaking becomes quantitatively important only if the electromagnetic fields are sufficiently strong. The breaking of scale invariance is larger for smaller values of the conductivity. Aspects of entropy production from charge diffusion currents and stability are also discussed.

23 pages, 14 figures. Revised discussion on entropy production, and new comparison plot with Strang-Splitting method

References in corpus (8)

• The Chiral Magnetic Effect
• Numerical magneto-hydrodynamics for relativistic nuclear collisions
• Multi-dimensional Numerical Scheme for Resistive Relativistic MHD
• Experimental searches for the chiral magnetic effect in heavy-ion collisions
• Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation
• New developments in relativistic magnetohydrodynamics
• Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory:a relaxation time approach
• Generalization of Bantilan-Ishi-Romatschke flow to Magnetohydrodynamics

Cited by in corpus (10)

• The regime of applicability of Israel-Stewart hydrodynamics
• Charge-dependent anisotropic flow in high-energy heavy-ion collisions from relativistic resistive magneto-hydrodynamic expansion
• Relativistic Dissipative Magnetohydrodynamics from the Boltzmann equation for a two-component gas
• Stability of multicomponent Israel-Stewart-Maxwell theory for charge diffusion
• Phenomenological Relativistic Second-Order Hydrodynamics for Multiflavor Fluids
• Transport Coefficients of relativistic matter: A detailed formalism with a gross knowledge of their magnitude
• Causality and stability in first-order conformal anisotropic hydrodynamics
• Relativistic resistive magnetohydrodynamics for a two-component plasma
• Generalized relativistic second order magnetohydrodynamics: A correlation function approach using Zubarev's nonequilibrium statistical operator
• Thermoelectric Conduction in General Relativity: A Causal, Stable, and Well Posed Theory