6 research outputs 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
SchrĂśdinger operators with δ and δâ˛-potentials supported on hypersurfaces
Self-adjoint SchrĂśdinger operators with δ and δâ˛-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the BirmanâSchwinger principle and a variant of Kreinâs formula are shown. Furthermore, Schattenâvon Neumann type estimates for the differences of the powers of the resolvents of the SchrĂśdinger operators with δ and δâ˛-potentials, and the SchrĂśdinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed SchrĂśdinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity
DLTS spectra of silicon diodes with p+-n-junction irradiated with high energy krypton ions
p+-n-Diodes have been studied. The diodes were manufactured on wafers (thickness 460 Οm, (111) plane) of uniformly phosphorus doped float-zone-grown single-crystal silicon. The resistivity of silicon was 90 âŚÂ cm and the phosphorus concentration was 5Ă1013 cmâ3. The diodes were irradiated with 250 MeV krypton ions. The irradiation fluence was 108 cmâ2. Deep-level transient spectroscopy (DLTS) was used to examine the defects induced by high energy krypton ion implantation. The DLTS spectra were recorded at a frequency of 1 MHz in the 78â290 K temperature range. The capacity-voltage characteristics have been measured at a reverse bias voltage from 0 to â19 V at a frequency of 1 MHz. We show that the main irradiation-induced defects are A-centers and divacancies. The behavior of DLTS spectra in the 150â260 K temperature range depends essentially on the emission voltage Ue. The variation of Ue allows us to separate the contributions of different defects into the DLTS spectrum in the 150â260 K temperature range. We show that, in addition to A-centers and divacancies, irradiation produces multivacancy complexes with the energy level Et = Ecâ(0.5Âą0.02) eV and an electron capture cross section of ~4Ă10â13 cm2
MALDI-TOF MS and Morphology Studies of Thiacalixarene-Silsesquioxane Products of Oligo- and Polycondensation
Spectral estimates for resolvent differences of self-adjoint elliptic operators
The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied