Riesz transform characterization of Hardy spaces associated with Schr\"odinger operators with compactly supported potentials

Let L=-\Delta+V be a Schr\"odinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\in H_L^1 if and only if R_j f \in L^1(R^d) for j=1,...,d, where R_j= \frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L.Comment: 6 page

Blood pressure and glaucoma: At the crossroads between cardiology and ophthalmology

Glaucoma is an optic nerve neuropathy of undetermined cause. Although many mechanisms are thought to be involved in the development and progression of the disease, only an increased intraocular pressure has been established as a clinically significant modifiable risk factor. Nevertheless, up to 40% of patients develop glaucoma without evidence of increased intraocular pressure.  Ample evidence suggests that alterations in the control of arterial blood might negatively affect optic nerve function. However, evidence-based guidelines on the management of arterial blood pressure in glaucoma patients are lacking. Regrettably, intraocular pressure is generally not included as a secondary end-point in clinical trials on arterial hypertension. Considering the relative simplicity of intraocular pressure measurements and large number of patients included in hypertension studies, the benefits of including intraocular pressure as a secondary end-point could be of a great value for improving care for glaucoma patients. Therefore, closer collaboration between cardiologists and ophthalmologists is needed.

Microscopic origin of diagonal stripe phases in doped nickelates

We investigate the electron density distribution and the stability of stripe phases in the realistic two-band model with hopping elements between e_g orbitals at Ni sites on the square lattice, and compare these results with those obtained for the doubly degenerate Hubbard model with two equivalent orbitals and diagonal hopping. For both models we determine the stability regions of filled and half-filled stripe phases for increasing hole doping x=2-n in the range of x<0.4, using Hartree-Fock approximation for large clusters. In the parameter range relevant to the nickelates, we obtain the most stable diagonal stripe structures with filling of nearly one hole per atom, as observed experimentally. In contrast, for the doubly degenerate Hubbard model the most stable stripes are somewhat reminiscent of the cuprates, with half-filled atoms at the domain wall sites. This difference elucidates the crucial role of the off-diagonal e_g hopping terms for the stripe formation in La_2-xSr_xNiO_4. The influence of crystal field is discussed as well.Comment: 15 pages, 12 figure

Simple test for quantum channel capacity

Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a given quantum channel. With this method we provide examples of quantum channels that can lead to high entanglement transmission but still have zero one-way capacity, in particular, regions of symmetric extendibility for isotropic states in arbitrary dimensions are presented. Further we derive {\it a new entanglement parameter} based on (normalised) relative entropy distance to the set of states that have symmetric extensions and show explicitly the symmetric extension of isotropic states being the nearest to singlets in the set of symmetrically extendible states. The suitable regularisation of the parameter provides a new upper bound on one-way distillable entanglement.Comment: 6 pages, no figures, RevTeX4. Signifficantly corrected version. Claim on continuity of channel capacities removed due to flaw in the corresponding proof. Changes and corrections performed in the part proposing a new upper bound on one-way distillable etanglement which happens to be not one-way entanglement monoton

Casimir effect for tachyonic fields

In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of Abel-Plana formula. Finaly, the Casimir energy and Casimir force as the functions of distance are obtained. In order to compare the resulting formula with the standard one, we calculate the Casimir energy and Casimir force for massive, scalar field.Comment: 7 pages, 9 figure

The DEEP2 Redshift Survey: Lyman Alpha Emitters in the Spectroscopic Database

We present the first results of a search for Lyman-alpha emitters (LAEs) in the DEEP2 spectroscopic database that uses a search technique that is different from but complementary to traditional narrowband imaging surveys. We have visually inspected ~20% of the available DEEP2 spectroscopic data and have found nine high-quality LAEs with clearly asymmetric line profiles and an additional ten objects of lower quality, some of which may also be LAEs. Our survey is most sensitive to LAEs at z=4.4-4.9 and that is indeed where all but one of our high-quality objects are found. We find the number density of our spectroscopically-discovered LAEs to be consistent with those found in narrowband imaging searches. The combined, averaged spectrum of our nine high-quality objects is well fit by a two-component model, with a second, lower-amplitude component redshifted by ~420 km/s with respect to the primary Lyman-alpha line, consistent with large-scale outflows from these objects. We conclude by discussing the advantages and future prospects of blank-sky spectroscopic surveys for high-z LAEs.Comment: Accepted for publication in Ap

Volume modulus inflation and a low scale of SUSY breaking

The relation between the Hubble constant and the scale of supersymmetry breaking is investigated in models of inflation dominated by a string modulus. Usually in this kind of models the gravitino mass is of the same order of magnitude as the Hubble constant which is not desirable from the phenomenological point of view. It is shown that slow-roll saddle point inflation may be compatible with a low scale of supersymmetry breaking only if some corrections to the lowest order Kahler potential are taken into account. However, choosing an appropriate Kahler potential is not enough. There are also conditions for the superpotential, and e.g. the popular racetrack superpotential turns out to be not suitable. A model is proposed in which slow-roll inflation and a light gravitino are compatible. It is based on a superpotential with a triple gaugino condensation and the Kahler potential with the leading string corrections. The problem of fine tuning and experimental constraints are discussed for that model.Comment: 28 pages, 8 figures, comments and references added, minor change in notation, version to be publishe