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We discuss the diffusion currents occurring in a dilute system and show that the charge currents do not only depend on gradients in the corresponding charge density, but also on the other conserved charges in the system—the diffusion currents are therefore coupled. Gradients in one charge thus generate dissipative currents in a different charge. In this approach, we model the Navier-Stokes term of the generated currents to consist of a diffusion coefficient matrix, in which the diagonal entries are the usual diffusion coefficients and the off-diagonal entries correspond to the coupling of different diffusion currents. We evaluate the complete diffusion matrix for a specific hadron gas and for a simplified quark-gluon gas, including baryon, electric and strangeness charge. Our findings are that the off-diagonal entries can range within the same magnitude as the diagonal ones.
We study the diffusion properties of the strongly interacting quark-gluon plasma (sQGP) and evaluate the diffusion coefficient matrix for the baryon (B), strange (S) and electric (Q) charges—κqq′ (q,q′=B,S,Q) and show their dependence on temperature T and baryon chemical potential μB. The nonperturbative nature of the sQGP is evaluated within the dynamical quasiparticle model (DQPM) which is matched to reproduce the equation of state of the partonic matter above the deconfinement temperature Tc from lattice QCD. The calculation of diffusion coefficients is based on two methods: (i) the Chapman-Enskog method for the linearized Boltzmann equation, which allows to explore nonequilibrium corrections for the phase-space distribution function in leading order of the Knudsen numbers as well as (ii) the relaxation time approximation (RTA). In this work we explore the differences between the two methods. We find a good agreement with the available lattice QCD data in case of the electric charge diffusion coefficient (or electric conductivity) at vanishing baryon chemical potential as well as a qualitative agreement with the recent predictions from the holographic approach for all diagonal components of the diffusion coefficient matrix. The knowledge of the diffusion coefficient matrix is also of special interest for more accurate hydrodynamic simulations.