Effect of Magnetic Field on the Phase Transition from Nuclear Matter to Quark Matter during Proto-Neutron Star Evolution

We have studied phase transition from hadron matter to quark matter in the presence of high magnetic fields incorporating the trapped electron neutrinos at finite temperatures. We have used the density dependent quark mass (DDQM) model for the quark phase while the hadron phase is treated in the frame-work of relativistic mean field theory. It is seen that the nuclear energy at phase transition decreases with both magnetic field and temperature. A brief discussion of the effect of magnetic field in supernova explosions and proto-neutron star evolution is given.