Diffusion coefficient matrix for multiple conserved charges: a Kubo approach

TL;DR

This paper derives Kubo relations for a diffusion matrix of multiple conserved charges in strongly interacting matter, linking microscopic quantum correlations to macroscopic charge diffusion behavior.

Contribution

It introduces a Kubo-based method to evaluate the diffusion matrix for multiple conserved charges, connecting it with kinetic theory in the weak coupling limit.

Findings

Kubo relations for diffusion matrix elements are derived.

Diffusion matrix reduces to kinetic theory results in weak coupling.

Toy model demonstrates the practical evaluation of the diffusion matrix.

Abstract

The strongly interacting matter created in relativistic heavy-ion collisions possesses several conserved quantum numbers, such as baryon number, strangeness, and electric charge. The diffusion process of these charges can be characterized by a diffusion matrix that describes the mutual influence of the diffusion of various charges. We derive the Kubo relations for evaluating diffusion coefficients as elements of a diffusion matrix. We further demonstrate that in the weak coupling limit, the diffusion matrix elements obtained through Kubo relations reduce to those obtained from kinetic theory with an appropriate identification of the relaxation times. We illustrate this evaluation in a toy model of two interacting scalar fields with two conserved charges.