Neutrino Mixing in Matter at Extreme High Energy

We have studied neutrino mixing at extreme high energy considering two flavour framework with matter effects. We analyze the atmospheric neutrino data within the simplest scheme of two neutrino oscillation. We consider as special case of matter density profile, which are relevant for neutrino oscillations. In particular, we compute to constrain a specific from of neutrino mass square difference and mixing in extreme high energy in matter. The dispersion relation for the neutrino mixing in neutrino oscillation in matter are discussed.