Speakers
Description
We study the dynamics of a heavy quark propagating through strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) plasma. Concretely, we calculate the complete momentum broadening probability distribution due to interactions with the plasma. This calculation includes and goes beyond the classic results for the drag coefficient $\eta_D$ and momentum diffusion coefficients $\kappa_T$, $\kappa_L$, and also allows one to read off the value of $\hat{q}$ for light-like particles. We use this probability distribution to derive the Kolmogorov equation (a generalized Fokker-Planck equation) that determines how the momentum distribution of heavy quarks evolves as they propagate through a thermal plasma. Our results display previously unquantified features about the dynamics of heavy quarks, such as the correlation between momentum broadening and energy loss, along with all of the higher order moments of the momentum broadening distribution. Most strikingly, we show that even though $\kappa_L$ and $\eta_D$ do not satisfy the fluctuation-dissipation relation, the stationary solution to the aforementioned Kolmogorov equation is, in fact, a Boltzmann distribution. All of the higher order moments of the broadening distribution contribute in an essential fashion to achieving kinetic equilibrium.
In the light of the many similarities between QCD at temperatures around $\Lambda_{\rm QCD}$ and $\mathcal{N}=4$ SYM, not least in the heavy quark momentum diffusion coefficient $\kappa$ as evidenced by recent lattice QCD calculations, we expect that this calculation in strongly coupled SYM plasma will serve as a useful reference point from which to gain intuition into the strongly coupled dynamics of QCD.
| Category | Theory |
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