Equilibration and hydrodynamics at strong and weak coupling

We give an updated overview of both weak and strong coupling methods to describe the approach to a plasma described by viscous hydrodynamics, a process now called hydrodynamisation. At weak coupling the very first moments after a heavy ion collision is described by the colour-glass condensate framework, but quickly thereafter the mean free path is long enough for kinetic theory to become applicable. Recent simulations indicate thermalization in a time t∼40(η/s)4/3/T [L. Keegan, A. Kurkela, P. Romatschke, W. van der Schee, Y. Zhu, Weak and strong coupling equilibration in nonabelian gauge theories, JHEP 04 (2016) 031. arXiv:1512.05347, doi:10.1007/JHEP04(2016)031], with T the temperature at that time and η/s the shear viscosity divided by the entropy density. At (infinitely) strong coupling it is possible to mimic heavy ion collisions by using holography, which leads to a dual description of colliding gravitational shock waves. The plasma formed hydrodynamises within a time of 0.41/T recent extension found corrections to this result for finite values of the coupling, when η/s is bigger than the canonical value of 1/4π, which leads to t∼(0.41+1.6(η/s−1/4π))/T [S. Grozdanov, W. van der Schee, Coupling constant corrections in holographic heavy ion collisions, arXiv:1610.08976]. Future improvements include the inclusion of the effects of the running coupling constant in QCD.