Diffusion processes involving multiple conserved charges: A study from kinetic theory and implications to the fluid-dynamical modeling of heavy ion collisions

Abstract

The bulk nuclear matter produced in heavy ion collisions carries a multitude of conserved quantum numbers: electric charge, baryon number, and strangeness. Therefore, the diffusion processes associated to these conserved charges cannot occur independently and must be described in terms of a set of coupled diffusion equations. This physics is implemented by replacing the traditional diffusion coefficients for each conserved charge by a diffusion coefficient matrix, which quantifies the coupling between the conserved quantum numbers. The diagonal coefficients of this matrix are the usual charge diffusion coefficients, while the off-diagonal entries describe the diffusive coupling of the charge currents. In this paper, we show how to calculate this diffusion coefficient matrix from kinetic theory and provide results for a hadron resonance gas and a gas of partons. We further find that the off-diagonal entries can reach similar magnitudes compared to the diagonal entries. In order to provide some insight on the influence that the coupling between the net charge diffusion currents can have on heavy ion observables, we present first results for the diffusive evolution of a hadronic system in a simple (1+1)D-fluid dynamics approach, and study different configurations of the diffusion matrix.

Transport properties of the strongly-interacting Quark-Gluon plasma

“…In the previous Subsections we have addressed the diffusion coefficients of the conserved baryon number and electric charge. Generally one should consider the full diffusion coefficient matrix (κ qq ′ , where q, q ′ = B, S, Q), which was introduced and evaluated for a hadron gas and a simple model for the QGP [52,104]. Since quarks carry more than one of the conserved charges, the diffusion current of each charge is no longer exclusively proportional to the gradient of the thermal potential ∇ µ µ q /T of that specific charge.…”

“…Furthermore, a first study on the impact of the coupling of baryon number and strangeness was provided in Ref. [104]. To this aim, the matrix of diffusion coefficients of hot and dense nuclear matter must be thoroughly investigated, as it is important for accurate hydrodynamic simulations.…”

“…We here combine the developments of Refs. [2,52,104] and evaluate the diffusion coefficient matrix of the strongly interacting non-perturbative QGP at finite (T, µ B ), with properties described by the DQPM model, based on a recently explored the Chapman-Enskog study [52,104,106]. This allows us to explore the influence of traces of non-equilibrium effects by accounting for the higher modes of the distribution function on the transport properties and compare the results with the often used kinetic RTA approximation.…”

“…We review first results for the diffusion coefficient matrix for the hot quark-gluon plasma at zero and finite baryon chemical potential µ B by applying the Chapman-Enskog method, described in detail in Refs. [52,104,106], to a strongly interacting QGP system described by the DQPM. This represents a significant and important improvement over the "simplified" model of a partonic system used in Refs.…”

“…This represents a significant and important improvement over the "simplified" model of a partonic system used in Refs. [52,104,106]. The Chapman-Enskog results are compared with the results for the diffusion coefficient matrix computed within the RTA approach based on the DQPM, and with several other models.…”