Glasma evolution and Bose-Einstein condensation with elastic and inelastic collisions

In this paper we investigate the role of inelastic collisions in the kinetic evolution of a highly overpopulated gluon system starting from a glasma-type initial condition. Using the Gunion-Bertsch formula we derive the inelastic collision kernel under the collinear and small-angle approximations. With both numerics and analytic analysis, we show that the inelastic process has two effects: globally changing (mostly reducing) the total particle number, while locally in the small-momentum regime always filling up the infrared modes extremely quickly. This latter effect is found to significantly speed up the emergence of a local thermal distribution in the infrared regime with vanishing local “chemical potential” and thus catalyze the onset of dynamical Bose-Einstein condensation to occur faster (as compared with the purely elastic case) in the overpopulated glasma.

Figure 1

(Left) A typical Feynman diagram contributing to ${\mathcal{C}}_{2\leftrightarrow 3}^a$: $p+1\leftrightarrow 2+3+k$. (Right) A typical Feynman diagram contributing to ${\mathcal{C}}_{2\leftrightarrow 3}^b$: $1+k+p\leftrightarrow 2+3$.

Figure 2

(Left) The distribution function $f(p)$ at different time moments during the evolution for purely inelastic collisions. (Right) The occupation at the smallest grid point $f(p=0.01Q_s)$ as a function of time for purely inelastic collisions.

Figure 3

The number density $n$ (left) and entropy density $s$ (right), both normalized by the corresponding equilibrium values, as a function of time for purely inelastic collisions.

Figure 4

(Left) The distribution function $f(p)$ at different time moments during evolution. (Right) The flux $S(p)$ defined in the elastic kernel at different time moments during evolution.

Figure 5

The inelastic kernel $C_{1\leftrightarrow 2}(p)$ (left) and $p^2{C}_{1\leftrightarrow 2}(p)$ (right) at different time moments during evolution.

Figure 6

The local thermal form parameters $T^{*}$ (left) and ${\mu }^{*}$ (right) as functions of time for different values of parameter $R$.

Figure 7

The occupation at the smallest grid point $f(p=0.005Q_s)$ as a function of time for different values of the parameter $R$.

Figure 8

(Left) The particle number density as a function of time for different values of the parameter $R$. (Right) The entropy density as a function of time for $R=1$ and $R=0$.

Figure 9

The local thermal form parameters $T^{*}$ (left) and ${\mu }^{*}$ (right) as functions of time for $z_c=0.2$, 0.5, 0.8 respectively.

Figure 10

The occupation at the smallest grid point $f(p=0.005Q_s)$ (left) and the particle number density (right) as functions of time for $z_c=0.2$, 0.5, 0.8 respectively.

Figure 11

A conjectured evolution of the condensate.

Figure 12

A typical Feynman diagram for $M_{2\leftrightarrow 3}$.