Electron transport in a two-terminal Aharonov-Bohm ring with impurities

Electron transport in a two-terminal Aharonov-Bohm ring with a few short-range scatterers is investigated. An analytical expression for the conductance as a function of the electron Fermi energy and magnetic flux is obtained using the zero-range potential theory. The dependence of the conductance on positions of scatterers is studied. We have found that the conductance exhibits asymmetric Fano resonances at certain energies. The dependence of the Fano resonances on magnetic field and positions of impurities is investigated. It is found that collapse of the Fano resonances occurs and discrete energy levels in the continuous spectrum appear at certain conditions. An explicit form for the wave function corresponding to the discrete level is obtained.Comment: 25 pages (one-column), 8 figure

Spin-hybrid-phonon resonance in anisotropic quantum dots

We have studied the absorption of electromagnetic radiation of an anisotropic quantum dot taking into account the spin-flip processes that is associated with the interaction of the electrons with optical phonons. It is shown that these processes lead to the resonance absorption. Explicit formula is derived for the absorption coefficient. The positions of the resonances peaks are found

Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Localization on quantum graphs with random vertex couplings

We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges

On the spectrum of gauge periodic point perturbations on the Lobachevsky plane

SIGLEAvailable from TIB Hannover: RR 1596(341) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The spectrum of periodic point perturbations and the Krein resolvent formula

We study periodic point perturbations, H, of a periodic elliptic operator H"0 on a connected complete non-compact Riemannian manifold X, endowed with an isometric, effective, properly discontinuous, and co-compact action of a discrete group #GAMMA#. Under some conditions of H"0, we prove that the gaps of the spectrum are labelled in a natural way by elements of the K_0-group of a certain C*-algebra. In particular, if the group #GAMMA# has the Kadison property then the spectrum has band structure. The Krein resolvent formula plays a crucial role in proving the main results. (orig.)Available from TIB Hannover: RR 1596(348) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman