64 research outputs found
New bounds on the Lieb-Thirring constants
Improved estimates on the constants , for ,
in the inequalities for the eigenvalue moments of Schr\"{o}dinger
operators are established
Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers
A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger
operators is established. The result is applied to prove spectral estimates on
trapped modes in quantum layers
Lieb-Thirring inequalities for geometrically induced bound states
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of
Schr\"odinger operators in wave guides with local perturbations. The estimates
are optimal in the weak-coupling case. To illustrate their applications, we
consider, in particular, a straight strip and a straight circular tube with
either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page
Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
We prove general comparison theorems for eigenvalues of perturbed Schrodinger
operators that allow proof of Lieb--Thirring bounds for suitable non-free
Schrodinger operators and Jacobi matrices.Comment: 11 page
Anomalous electron trapping by localized magnetic fields
We consider an electron with an anomalous magnetic moment g>2 confined to a
plane and interacting with a nonzero magnetic field B perpendicular to the
plane. We show that if B has compact support and the magnetic flux in the
natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F]
bound states, without making any assumptions about the field profile.
Furthermore, in the zero-flux case there is a pair of bound states with
opposite spin orientations. Using a Birman-Schwinger technique, we extend the
last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-\delta})
correcting thus a recent result. Finally, we show that under mild regularity
assumptions the existence can be proved for non-symmetric fields with tails as
well.Comment: A LaTeX file, 12 pages; to appear in J. Phys. A: Math. Ge
Weakly coupled bound states of Pauli operators
We consider the two-dimensional Pauli operator perturbed by a weakly coupled,
attractive potential. We show that besides the eigenvalues arising from the
Aharonov-Casher zero modes there are two or one (depending on whether the flux
of the magnetic field is integer or not) additional eigenvalues for arbitrarily
small coupling and we calculate their asymptotics in the weak coupling limit.Comment: 19 page
Cosmic-ray pitch-angle scattering in imbalanced mhd turbulence simulations
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic
(MHD) simulations with imbalanced turbulence are calculated for fully evolving
electromagnetic turbulence. We compare with theoretical predictions derived
from the quasilinear theory of cosmic-ray diffusion for an idealized slab
spectrum and demonstrate how cross helicity affects the shape of the
pitch-angle diffusion coefficient. Additional simulations in evolving magnetic
fields or static field configurations provide evidence that the scattering
anisotropy in imbalanced turbulence is not primarily due to coherence with
propagating Alfven waves, but an effect of the spatial structure of electric
fields in cross-helical MHD turbulence.Comment: 13 pages, 15 figures. Accepted by Ap
Nanoinformatics knowledge infrastructures: bringing efficient information management to nanomedical research
Nanotechnology represents an area of particular promise and significant opportunity across multiple scientific disciplines. Ongoing nanotechnology research ranges from the characterization of nanoparticles and nanomaterials to the analysis and processing of experimental data seeking correlations between nanoparticles and their functionalities and side effects. Due to their special properties, nanoparticles are suitable for cellular-level diagnostics and therapy, offering numerous applications in medicine, e.g. development of biomedical devices, tissue repair, drug delivery systems and biosensors. In nanomedicine, recent studies are producing large amounts of structural and property data, highlighting the role for computational approaches in information management. While in vitro and in vivo assays are expensive, the cost of computing is falling. Furthermore, improvements in the accuracy of computational methods (e.g. data mining, knowledge discovery, modeling and simulation) have enabled effective tools to automate the extraction, management and storage of these vast data volumes. Since this information is widely distributed, one major issue is how to locate and access data where it resides (which also poses data-sharing limitations). The novel discipline of nanoinformatics addresses the information challenges related to nanotechnology research. In this paper, we summarize the needs and challenges in the field and present an overview of extant initiatives and efforts
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