The transmission probability of quasi-particles in an ultra-cold superfluid contained two channels: the effects of size of system, within the BCS quasi-classical approximation

Of central importance in ultra-cold Fermi superfluids contained two channels with different energies, is the study of effects of size of system on different physical parameters. One of the important parameters in these systems is the interface transmission probability between superfluid and normal phases. In this paper, by using the Bogoliubov equations and the first order perturbation for two channels and also by considering the approximation related to deep BCS region for quasi-particles momentum and quasi-holes momentum, the effects of size of system, which is expressed within the quasi-classical approximation, are calculated on interface transmission coefficient of two channels of ultra-cold system and the physical diagrams are separately plotted and compared.