Frustration, interaction strength and ground-state entanglement in complex quantum systems

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.Comment: 11 pages, 3 figure

Entropic uncertainty relations and entanglement

We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty relation on one part of the system results in a separability condition on the composite system. We investigate the resulting criteria using the Tsallis entropy for two and three qubits.Comment: 8 pages, 3 figures, v2: small change

A Detailed Analysis of a Cygnus Loop Shock-Cloud Interaction

The XA region of the Cygnus Loop is a complex zone of radiative and nonradiative shocks interacting with interstellar clouds. We combine five far ultraviolet spectral observations from the Hopkins Ultraviolet Telescope (HUT), a grid of 24 IUE spectra and a high-resolution longslit Halpha spectrum to study the spatial emission line variations across the region. These spectral data are placed in context using ground-based, optical emission line images of the region and a far-UV image obtained by the Ultraviolet Imaging Telescope (UIT). The presence of high-ionization ions (OVI, NV, CIV) indicates a shock velocity near 170 km/s while other diagnostics indicate v_shock=140 km/s. It is likely that a large range of shock velocities may exist at a spatial scale smaller than we are able to resolve. By comparing CIV 1550, CIII 977 and CIII] 1909, we explore resonance scattering across the region. We find that a significant column depth is present at all positions, including those not near bright optical/UV filaments. Analysis of the OVI doublet ratio suggests an average optical depth of about unity in that ion while flux measurements of [SiVIII] 1443 suggest a hot component in the region at just below 10^6K. Given the brightness of the OVI emission and the age of the interaction, we rule out the mixing layer interpretation of the UV emission. Furthermore, we formulate a picture of the XA region as the encounter of the blast wave with a finger of dense gas protruding inward from the pre-SN cavity.Comment: 21 pages, 9 figures, accepted by the Astronomical Journal, July 2001 Full resolution figures available at http://fuse.pha.jhu.edu/~danforth/xa

Ligand Exchange Reactions in Some Pentaamminecobalt(III) Complexes

966-96

Sparse Projections of Medical Images onto Manifolds

Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of-sample extensions are applied by constructing an interpolation function that maps from the input space to the low-dimensional manifold. Commonly used approaches such as the Nyström extension and kernel ridge regression require using all training points. We propose an interpolation function that only depends on a small subset of the input training data. Consequently, in the testing phase each new point only needs to be compared against a small number of input training data in order to project the point onto the low-dimensional space. We interpret our method as an out-of-sample extension that approximates kernel ridge regression. Our method involves solving a simple convex optimization problem and has the attractive property of guaranteeing an upper bound on the approximation error, which is crucial for medical applications. Tuning this error bound controls the sparsity of the resulting interpolation function. We illustrate our method in two clinical applications that require fast mapping of input images onto a low-dimensional space.National Alliance for Medical Image Computing (U.S.) (grant NIH NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (grant NIH NCRR NAC P41-RR13218)National Institutes of Health (U.S.) (grant NIH NIBIB NAC P41-EB-015902

Many parameter Hoelder perturbation of unbounded operators

If $u\mapsto A(u)$ is a $C^{0,\alpha}$-mapping, for $0< \alpha \le 1$, having as values unbounded self-adjoint operators with compact resolvents and common domain of definition, parametrized by $u$ in an (even infinite dimensional) space, then any continuous (in $u$) arrangement of the eigenvalues of $A(u)$ is indeed $C^{0,\alpha}$ in $u$.Comment: LaTeX, 4 pages; The result is generalized from Lipschitz to Hoelder. Title change

Topical and Systemic Effects of Retinoids on Horn-Filled Utriculus Size in the Rhino Mouse. A Model to Quantify “Antikeratinizing” Effects of Retinoids

A method was developed to quantify the “antikeratinizing” effects of various retinoids (all-trans-retinoic acid, 13-cis-retinoic acid, motretinide, etretinate) in rhino mouse skin, which contains many keratinized pilosebaceous structures or horn-filled utriculi. Mean utriculus diameters in whole mount epidermis were determined and dose-response relationships were constructed after topical or oral administration of test retinoids. All- trans-retinoic acid was 3.7×, 12.5×, and 50× more potent than 13-cis-retinoic acid, etretinate, and motretinide, respectively, after topical administration. Administered orally, all-trans-retinoic acid was 2.3× more potent than 13-cis-retinoic acid At 5 mg/kg, each retinoid produced a significant reduction in utriculus size. The rhino mouse model represents a novel and useful assay to quantify antikeratinizing activity and potency differences of biologically active retinoids

Tri-n-butylphosphate Solvent System: Mechanism of Solvolytic & Substitution Reactions in Tri-n-burylphosphate

379-38

CHIANTI - an Atomic Database for Emission Lines. Paper VI: Proton Rates and Other Improvements

The CHIANTI atomic database contains atomic energy levels, wavelengths, radiative transition probabilities and electron excitation data for a large number of ions of astrophysical interest. Version 4 has been released, and proton excitation data is now included, principally for ground configuration levels that are close in energy. The fitting procedure for excitation data, both electrons and protons, has been extended to allow 9 point spline fits in addition to the previous 5 point spline fits. This allows higher quality fits to data from close-coupling calculations where resonances can lead to significant structure in the Maxwellian-averaged collision strengths. The effects of photoexcitation and stimulated emission by a blackbody radiation field in a spherical geometry on the level balance equations of the CHIANTI ions can now be studied following modifications to the CHIANTI software. With the addition of H I, He I and N I, the first neutral species have been added to CHIANTI. Many updates to existing ion data-sets are described, while several new ions have been added to the database, including Ar IV, Fe VI and Ni XXI. The two-photon continuum is now included in the spectral synthesis routines, and a new code for calculating the relativistic free-free continuum has been added. The treatment of the free-bound continuum has also been updated.Comment: CHIANTI is available at http://wwwsolar.nrl.navy.mil/chianti.htm