We will formulate a macroscopic theory of Superfluidity, using a particular constitutive equation of differential form which we will demonstrate to be equivalent to a non-local relation between the stress and the density.
We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.