Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Dynamics of Entanglement and the Schmidt Gap in a Driven Light-Matter System

The ability to modify light-matter coupling in time (e.g. using external pulses) opens up the exciting possibility of generating and probing new aspects of quantum correlations in many-body light-matter systems. Here we study the impact of such a pulsed coupling on the light-matter entanglement in the Dicke model as well as the respective subsystem quantum dynamics. Our dynamical many-body analysis exploits the natural partition between the radiation and matter degrees of freedom, allowing us to explore time-dependent intra-subsystem quantum correlations by means of squeezing parameters, and the inter-subsystem Schmidt gap for different pulse duration (i.e. ramping velocity) regimes -- from the near adiabatic to the sudden quench limits. Our results reveal that both types of quantities indicate the emergence of the superradiant phase when crossing the quantum critical point. In addition, at the end of the pulse light and matter remain entangled even though they become uncoupled, which could be exploited to generate entangled states in non-interacting systems.Comment: 15 pages, 4 figures, Accepted for publication in Journal of Physics B, special issue Correlations in light-matter interaction

Static and Dynamic Spectroscopy of (Al,Ga)As/GaAs Microdisk Lasers with Interface Fluctuation Quantum Dots

We have studied the steady state and dynamic optical properties of semiconductor microdisk lasers whose active region contains interface fluctuation quantum dots in GaAs/(Ga,Al)As quantum wells. Steady-state measurements of the stimulated emission via whispering gallery modes yield a quality factor $Q \sim 5600$ and a coupling constant $\beta \sim 0.09$. The broad gain spectrum produces mode hopping between spectrally adjacent whispering gallery modes as a function of temperature and excitation power. Time- and energy-resolved photoluminescence measurements show that the emission rise and decay rates increase significantly with excitation power. Marked differences are observed between the radiative decay rates in processed and unprocessed samples.Comment: To appear in Phys. Rev.

Magnetoresistance Anomalies in (Ga,Mn)As Epilayers with Perpendicular Magnetic Anisotropy

We report the observation of anomalies in the longitudinal magnetoresistance of tensile-strained (Ga,Mn)As epilayers with perpendicular magnetic anisotropy. Magnetoresistance measurements carried out in the planar geometry (magnetic field parallel to the current density) reveal "spikes" that are antisymmetric with respect to the direction of the magnetic field. These anomalies always occur during magnetization reversal, as indicated by a simultaneous change in sign of the anomalous Hall effect. The data suggest that the antisymmetric anomalies originate in anomalous Hall effect contributions to the longitudinal resistance when domain walls are located between the voltage probes. This interpretation is reinforced by carrying out angular sweeps of $\vec{H}$, revealing an antisymmetric dependence on the helicity of the field sweep.Comment: Submitted to Phys. Rev.

Estrogen-related genes and postmenopausal osteoporosis risk

Background To date, more than 150 candidate genes related to osteoporosis have been described, but osteoporosis has increasingly been considered a polygenic disease modulated by environmental factors. It is thought that osteoporosis predisposition, pathology, and treatment response depend on the interaction between different genes or between genes and environmental factors. Objective The aim of this study was to evaluate the relationship between the presence of single nucleotide polymorphisms (SNPs) in the estrogen metabolic pathway and the development of osteoporosis and to determine whether this relationship is monogenic or whether interactions between genes exist. Materials and methods A multicentric study with 1980 postmenopausal Spanish women in fi ve Spanish communities was conducted. The women completed a specifi c questionnaire that inquired about risk factors for osteoporosis. Data on participants ’ bone mineral density were obtained with dual-energy X-ray densitometers, and genetic data were obtained from frozen peripheral blood. Results The digenic protection combinations indicated involvement of the wild-type genotype (WT) of the 3 UTR marker for the CYP19A1 gene, the IVS4 marker of the same gene, and the BMP15 and FSHR genes. Among patients who carried two or more of the genotypes considered ‘ risky ’ , the triple combination among markers of the ESR2 and NRIP1 genes with any of the two mutations of the analyzed markers of the BMP15 gene gave a mean T -score value of 2.32 0.91 ( p 0.02). Conclusion Variants of the new candidate genes ( NRIP and BMP15 ) can predispose patients to osteoporosis