content_image/346425.jpg content_image/346431.jpg content_image/346432.jpg content_image/346433.jpg content_image/346434.jpg
<img src='content_image/346425.jpg'>

a pseudo-energy ε$_{a}$ ( k ) for each type of particle and the filling fractions: 

<img src='content_image/346431.jpg'>

As shown in Appendix B, in our approximation, the pseudo-energies satisfy the coupled integral equations: 

where ω$_{a}$ ( k ) = k $^{2}$/ 2 m$_{a}$ , 

and G$_{ab}$ is the 2-body scattering kernel. By Galilean invariance, the kernel is a function of | v$_{a}$ − v$_{b}$ | where v = k/m is a velocity. For any function g we defined: 

<img src='content_image/346432.jpg'>

<img src='content_image/346433.jpg'>

<img src='content_image/346434.jpg'>

