Fermions in low-dimensional systems and the transition between bulk and surface properties

Abstract

We discuss three formalisms for the description of Fermions in low-dimensional systems. Then we consider dimensionally hybrid Hamiltonians with mixed three-dimensional and two-dimensional kinetic terms. These Hamiltonians yield particular dimensionally hybrid Green’s functions with interesting prospects for the description of the transition between two-dimensional and three-dimensional behavior of particles in the presence of attractive interface potentials.PACS Nos.: 05.30.Fk, 71.10.Pm, 73.20.–r