Excitations of Quantum Fluid 3He Confined to Cylindrical Shells

The general features of the thermodynamics and dynamics of Fermi fluids confined to cylindrical shells, like those produced by the adsorption of helium in the inner surfaces of carbon nanotubes, are examined, with emphasis on the dispersion relations and main characteristics of the excitation spectrum of fluid ^3He in such environments. The thermodynamics of fermions with band single-particle spectrum is reviewed discussing the specific aspects of the curved manifold. The Linhard function for one and quasi-onedimensional Landau quasiparticles with cylindrical band spectrum is presented. Among the various branches of zero sound excitations induced by polarization potentials, undamped spin zero sound is a new outcome, made possible by the particular geometry.