Description of Bose-Einstein condensate of cold gas in interaction through virtual states of non-condensate atomic components

We study the nonlinear interaction between two species of Bose gases having a large mass imbalance. It is presented the situation, when at low temperature, one of gas component, with smallest mass, is Bose-Einstein condensed, while the other gas is not. We show that the new interaction Hamiltonian with temperature dependent potential part takes into account all binary exchange energy between the atoms of the smallest mass component through the virtual states of non-condensate components. The modification of the traditional phase transition representation of the number of atoms in the condensate as a function of the temperature is described by an anomaly in the low temperature branch of this dependence. This anomaly have the tendency of the increasing of the numbers of atoms in condensate with increasing of temperature for a small value of the relative parameter T∕Tc, where Tc is the critical temperature of the phase transition.