Vacuum block thermalization in semi-classical 2d CFT

The universal nature of black hole collapse in asymptotically AdS(3) gravitational theories suggests that its holographic dual process, thermalization, should similarly be fixed by the universal features of 2d CFT with large central charge c. It is known that non-equilibrium states with scaling dimensions of order c can be sorted into states that eventually thermalize and those that fail to do so. By proving an equivalence between bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's equation it is shown that semi-classical CFTs possess a phase transition where a state that fails to thermalize can be promoted to a thermalizing state by preparing the system beforehand with an energy greater than an appropriate threshold energy. It is generally a difficult problem to ascertain whether a state will thermalize or not. As partial progress to this problem a set of lower bounds are presented for the threshold energy, which can alternatively be interpreted as criteria for thermalization.