Interference effects between the initial and final state radiation in a QCD medium

Coherence between multiple emitters is one of the most remarkable properties of QCD jet physics in vacuum. In the presence of a QCD medium one expects that the coherence pattern between multiple emitters is affected. In this work we calculate the gluon emission spectrum off an "asymptotic quark" traversing a dilute QCD medium. When interferences between initial and final quark are included, the medium induced gluon distribution gets modified. The coherent, incoherent and soft limit of the medium induced spectrum are studied. In the soft limit we find an elegant and intuitive probabilistic interpretation. We comment on possible phenomenological applications of this setup for studying coherence effects on observables studied in high energy nuclear collisions.