Inhomogeneous system Contact interaction 4 Electron gas 4 Equations of motion 4 Fermions 4 Local density approximation 4 Mean field approximation 4 Particle currents 4 Particle densities 4 Scattering length 4 Thomas-Fermi approximation 4 Trapped fermi gas 4 Adsorption 2 First order 2 Grand canonical ensemble 2 Hard spheres 2 Hard-sphere system 2 Partition functions 2 Spheres 2 Spherical cavities 2 Spherical objects 2 Surface tension 2 Thermodynamic properties 2