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To understand the dynamics of thermalization in heavy ion collisions in theperturbative framework it is essential to first find corrections to thefree-streaming classical gluon fields of the McLerran-Venugopalan model. Thecorrections that lead to deviations from free streaming (and that dominate atlate proper time) would provide evidence for the onset of isotropization (and,possibly, thermalization) of the produced medium. To find such corrections wecalculate the late-time two-point Green function and the energy-momentum tensordue to a single $2 \to 2$ scattering process involving two classical fields. Tomake the calculation tractable we employ the scalar $\varphi^4$ theory insteadof QCD. We compare our exact diagrammatic results for these quantities to thosein kinetic theory and find disagreement between the two. The disagreement is inthe dependence on the proper time $\tau$ and, for the case of the two-pointfunction, is also in the dependence on the space-time rapidity $\eta$: theexact diagrammatic calculation is, in fact, consistent with the free streamingscenario. Kinetic theory predicts a build-up of longitudinal pressure, which,however, is not observed in the exact calculation. We conclude that we find noevidence for the beginning of the transition from the free-streaming classicalfields to the kinetic theory description of the produced matter after a single$2 \to 2$ rescattering.

Time-Dependent Observables in Heavy Ion Collisions II: in Search of Pressure Isotropization in the $\varphi^4$ Theory