Covariant transport theory approach to elliptic flow in relativistic heavy ion collision

We present a new direct simulation Monte Carlo method for solving the relativistic Boltzmann equation. We solve numerically the two-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport calculation smoothly converges toward the value from ideal hydrodynamics as the number of collisions per particle increases, as expected on general theoretical grounds but in contrast with previous transport calculations.

Figure 1

Picture of a collision between a particle 1 of size $\sigma =2r$ and a pointlike particle 2. The impact parameter $d$, as defined in Eq. (3), is negative.

Figure 2

Variation of the elliptic flow $v_2$ with the Knudsen number, $\mathrm{Kn}$, for several values of the dilution parameter $D$. The statistical error on each point is $\delta v_2=7\times {10}^{-4}$. For each value of $D$, Monte Carlo results are fitted using Eq. (9).

Figure 3

Time dependence of the average elliptic flow $v_2$ from the transport model, from the corresponding two-dimensional hydro calculation, and from usual three-dimensional hydro with Bjorken longitudinal expansion.