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

On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2

Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional Schr\"odinger operator $Hu:=-u^{\prime\prime}-Vu,\ V\geq 0,$ on $L_2({\Bbb R})$. We prove the inequality \sum_i|E_i(H)|^\gamma\leq L_{\gamma,1}\int_{\Bbb R} V^{\gamma+1/2}(x)dx, (1) for the "limit" case $\gamma=1/2.$ This will imply improved estimates for the best constants $L_{\gamma,1}$ in (1), as $1/2<\gamma<3/2.Comment: AMS-LATEX, 15 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

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