Dynamic equation for condensate of electron-hole pairs in a two-layer graphene system

In two-layer graphene systems the electron-hole pairs with spatially separated components make a transition to a superfluid state at low temperatures. A microscopic derivation of the dynamic equation for condensate wave function of electron-hole pairs is presented. On the basis of the spectrum of elementary excitations the superfluid transition temperature is calculated for a wide range of interlayer distances and magnetic fields.