Ashutosh Dash (Frankfurt)

On the validity of Ohm's law in relativistic plasmas

Relativistic plasmas play a significant role in high-energy phenomena, including heavy-ion collisions, black-hole magnetospheres, relativistic jets, and the early universe. The coarse- grained framework for describing the motion of charged fluid is known as relativistic magneto-hydrodynamics (MHD). The MHD equations, which comprise the particle conservation law, the energy/momentum conservation laws, and Maxwell’s equations, must also be complemented by Ohm’s law. The usual Navier-Stokes form of Ohm's law is acausal and needs to be replaced with an evolution equation of the charge diffusion current with a finite relaxation time, 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 electrical conductivity and the charge-diffusion relaxation time. We will investigate in a simplified 1+1-dimensional setting in the context of heavy-ion collision, where matter and electromagnetic fields are assumed to be transversely homogeneous and are initially expanding according to a Björken scaling. We will see how the scale invariance is broken by the ensuing self-consistent dynamics of matter and electromagnetic fields. Implications of these findings on the recent measurement of charged particle directed flow by the STAR experiment will also be discussed.