33,288 research outputs found
On Local Borg-Marchenko Uniqueness Results
We provide a new short proof of the following fact, first proved by one of us
in 1998: If two Weyl-Titchmarsh m-functions, , of two Schr\"odinger
operators H_j = -\f{d^2}{dx^2} + q_j, j=1,2 in , , are exponentially close, that is, |m_1(z)- m_2(z)|
\underset{|z|\to\infty}{=} O(e^{-2\Ima (z^{1/2})a}), 0<a<R, then
a.e.~on . The result applies to any boundary conditions at x=0 and x=R
and should be considered a local version of the celebrated Borg-Marchenko
uniqueness result (which is quickly recovered as a corollary to our proof).
Moreover, we extend the local uniqueness result to matrix-valued Schr\"odinger
operators.Comment: LaTeX, 18 page
Electron spin dynamics and electron spin resonance in graphene
A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba,
and ripple spin-orbit coupling is presented. We find from spin relaxation data
by Tombros et al. [Nature 448, 571 (2007).] that intrinsic spin-orbit coupling
dominates over other contributions with a coupling constant of 3.7 meV.
Although it is 1-3 orders of magnitude larger than those obtained from first
principles, we show that comparable values are found for other honeycomb
systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance
(ESR). We predict that spin coherence is longer preserved for spins
perpendicular to the graphene plane, which is beneficial for spintronics. We
identify experimental conditions when bulk ESR is realizable on graphene
Core drill's bit is replaceable without withdrawal of drill stem - A concept
Drill bit is divided into several sectors. When collapsed, the outside diameter is forced down the drill stem, when it reaches bottom the sectors are forced outward and form a cutting bit. A dulled bit is retracted by reversal of this procedure
Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
We present examples of rooted tree graphs for which the Laplacian has
singular continuous spectral measures. For some of these examples we further
establish fractional Hausdorff dimensions. The singular continuous components,
in these models, have an interesting multiplicity structure. The results are
obtained via a decomposition of the Laplacian into a direct sum of Jacobi
matrices
On the Hierarchical Preconditioning of the Combined Field Integral Equation
This paper analyzes how hierarchical bases preconditioners constructed for
the Electric Field Integral Equation (EFIE) can be effectively applied to the
Combined Field Integral Equation (CFIE). For the case where no hierarchical
solenoidal basis is available (e.g., on unstructured meshes), a new scheme is
proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz
subspace by using a Helmholtz projector, while a hierarchical non-solenoidal
basis is used for the non-solenoidal Helmholtz subspace. This results in a
well-conditioned system. Numerical results corroborate the presented theory
Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics
A new method is presented to study supersymmetric quantum mechanics. Using relative scattering techniques, basic relations are derived between Kreinâs spectral shift function, the Witten index, and the anomaly. The topological invariance of the spectral shift function is discussed. The power of this method is illustrated by treating various models and calculating explicitly the spectral shift function, the Witten index, and the anomaly. In particular, a complete treatment of the twoâdimensional magnetic field problem is given, without assuming that the magnetic flux is quantized
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