Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Electric-field induced capillary interaction of charged particles at a polar interface

We study the electric-field induced capillary interaction of charged particles at a polar interface. The algebraic tails of the electrostatic pressure of each charge results in a deformation of the interface $u\sim \rho ^{-4}$. The resulting capillary interaction is repulsive and varies as $\rho ^{-6}$ with the particle distance. As a consequence, electric-field induced capillary forces cannot be at the origin of the secondary minimum observed recently for charged PMMA particles at on oil-water interface.Comment: June 200

Suppression of electron scattering resonances in graphene by quantum dots

Transmission of low-energetic electrons through two-dimensional materials leads to unique scattering resonances. These resonances contribute to photoemission from occupied bands where they appear as strongly dispersive features of suppressed photoelectron intensity. Using angle-resolved photoemission we have systematically studied scattering resonances in epitaxial graphene grown on the chemically differing substrates Ir(111), Bi/Ir, Ni(111) as well as in graphene/Ir(111) nanopatterned with a superlattice of uniform Ir quantum dots. While the strength of the chemical interaction with the substrate has almost no effect on the dispersion of the scattering resonances, their energy can be controlled by the magnitude of charge transfer from/to graphene. At the same time, a superlattice of small quantum dots deposited on graphene eliminates the resonances completely. We ascribe this effect to a nanodot-induced buckling of graphene and its local rehybridization from sp$^{2}$ to sp$^{3}$ towards a three-dimensional structure. Our results suggest nanopatterning as a prospective tool for tuning optoelectronic properties of two-dimensional materials with graphene-like structure.Comment: The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.or

Bunching Transitions on Vicinal Surfaces and Quantum N-mers

We study vicinal crystal surfaces with the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of phases in which steps coalesce into bunches of n steps each. The value of n varies with temperature and the ratio of short to long range interaction strengths. We propose that the bunch phases have been observed in very recent experiments on Si surfaces. Within the context of a mapping of the model to a system of bosons on a 1D lattice, the bunch phases appear as quantum n-mers.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let

Qualitative features of periodic solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree