Localized two-particle states in deformed nanolayers

Problem of particles storage in nanolayered structure is considered. Local deformations of the nanolayers leads to appearance of eigenvalues of the corresponding one-particle Hamiltonian. The cardinality of the discrete spectrum is used to estimate the maximal number of non-interacting fermions stored in the nanolayers. The discrete spectrum of the Hamiltonian of two interacting particles is considered. Relation between the system parameters (interaction intensity - waveguide deformation) ensuring the existence of non-empty discrete spectrum is studied. Hartree method and FEM are used.