Causal baryon diffusion and colored noise

We construct a model of baryon diffusion which has the desired properties of causality and analyticity. The model also has the desired property of colored noise, meaning that the noise correlation function is not a Dirac delta function in space and time; rather, it depends on multiple time and length constants. The model can readily be incorporated in 3+1-dimensional second-order viscous hydrodynamical models of heavy-ion collisions, which is particularly important at beam energies where the baryon density is large.

Figure 1

The regular part of the dimensionless baryon correlator $f_{\mathrm{reg}}(\widehat{r},\widehat{t})$ for the Cattaneo equation. The correlator is shown for $\widehat{t}=0.5$ (dashed line), $\widehat{t}=1$ (solid line), and $\widehat{t}=1.5$ (dotted line).

Figure 2

The regular part of the dimensionless baryon correlator $f_{\mathrm{reg}}(\widehat{r},\widehat{t})$ for the Gurtin-Pipkin equation with $x=3$. The correlator is shown for $\widehat{t}=0.5$ (dashed line), $\widehat{t}=1$ (solid line), and $\widehat{t}=1.5$ (dotted line).

Figure 3

The regular part of the dimensionless baryon correlator $f_{\mathrm{reg}}(\widehat{r},\widehat{t})$ for the Gurtin-Pipkin equation with $x=1$. The correlator is shown for $\widehat{t}=0.5$ (dashed line), $\widehat{t}=1$ (solid line), and $\widehat{t}=1.5$ (dotted line).

Figure 4

The regular part of the dimensionless noise correlator $g_{\mathrm{reg}}(\widehat{r},\widehat{t})$ for $x=3$. The correlator is shown for $\widehat{t}=0.5$ (dashed line), $\widehat{t}=1$ (solid line), and $\widehat{t}=1.5$ (dotted line).

Figure 5

The regular part of the dimensionless noise correlator $g_{\mathrm{reg}}(\widehat{r},\widehat{t})$ for $x=1$. The correlator is shown for $\widehat{t}=0.5$ (dashed line), $\widehat{t}=1$ (solid line), and $\widehat{t}=1.5$ (dotted line).