Intriguing examples of inhomogeneous broadening

Three problems are considered in which inhomogeneous broadening can yield unusual consequences. One problem involves the energy levels of atoms moving within nanopores of nearly cylindrical cross section. A second involves atomic or molecular motion in a quasi-one-dimensional interstitial channel within a bundle of carbon nanotubes. The third problem involves motion within a groove between two nanotubes at the surface of such a bundle. In each case, the density of states at low energy is qualitatively different from that occurring in the perfectly homogeneous case.