Nonlinear dynamics of jet quenching

We present an analytic framework for jet quenching in dense QCD matter that unifies medium-induced branching with vacuum collinear evolution. Energy transported outside the jet region is governed by a non-linear rate equation that resums arbitrary-angle gluon splittings, each enhanced by the medium length $L$. We show that for asymptotically large energies the energy-loss distribution for a single hard parton exhibits an exponential (generalized Poisson) behavior that provides the initial condition for a non-linear, DGLAP-like evolution that resums collinear logarithms associated with early in-vacuum fragmentation and with the angular resolution of the medium. This framework allows a systematic resummation of parton branching contributions to jet energy loss.