Energetics of an interacting electron system on a surface

We present some properties of an interacting N-fermion system on a cylindrical surface focusing in the quantum mechanical size effects of the ground-state observables. We use an effective zero-range two-fermion interaction which allows for an analytical Hartree-Fock approach. Within this model, quantum size effects can be understood as a consequence of filling states in the Fermi sea in which naturally arises a clear dependence on the Fermi momentum and the cylinder radius. Particularly, the model shows that the difference between the surface and bulk energies does not depend on the strength interaction. A relationship between the chemical potential and the bulk energy is analytically derived. The approach is also suitable for carbon nanotubes.