Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed anisotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, the beta factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.Comment: 5 pages, 3 figure

Dielectric structures with bound modes for microcavity lasers

Cavity modes of dielectric microspheres and vertical cavity surface emitting lasers, in spite of their high Q, are never exactly bound, but have a finite width due to leakage at the borders. We propose types of microstructures that sustain three-dimensionally bound modes of the radiation field when dissipation is neglected. Unlike photonic crystals, the photonic systems that we consider here rely on periodicity in only one or two dimensions. In particular, we discuss a cavity composed of two crossed vertical layers combined with a periodic structure of horizontal layers. The layers have an anisotropic dielectric tensor, which could be obtained by making air holes in the vertical and horizontal directions within isotropic material. We calculate cavity resonance frequencies and spontaneous emission rates. The simplicity of this laser geometry allows an analytical study of light propagation and amplification in three dimensions

Entangled photons from small quantum dots

We discuss level schemes of small quantum-dot turnstiles and their applicability in the production of entanglement in two-photon emission. Due to the large energy splitting of the single-electron levels, only one single-electron level and one single-hole level can be made resonant with the levels in the conduction band and valence band. This results in a model with nine distinct levels, which are split by the Coulomb interactions. We show that the optical selection rules are different for flat and tall cylindrically symmetric dots, and how this affects the quality of the entanglement generated in the decay of the biexciton state. The effect of charge-carrier tunneling and of a resonant cavity is included in the model

Spectroscopic factors for nucleon knock-out from 16O at small missing energy.

Spectroscopic factors for one-nucleon knock-out fro

Selectivity of the {16}O(e,e'pp) reaction to discrete final states.

Resolution of discrete final states in the $^{16}$O(e,e$'$pp)$^{14}$C reaction may provide an interesting tool to discriminate between contributions from one- and two-body currents in this reaction. This is based on the observation that the $0^+$ ground state and first $2^+$ state of $^{14}$C are reached predominantly by the removal of a $^1S_0$ pair from $^{16}$O in this reaction, whereas other states mostly arise by the removal of a $^3P$ pair. This theoretical prediction has been supported recently by an analysis of the pair momentum distribution of the experimental data. In this paper we present results of reaction calculations performed in a direct knock-out framework where final-state interaction and one- and two-body currents are included. The two-nucleon overlap integrals are obtained from a calculation of the two-proton spectral function of $^{16}$O and include both long-range and short-range correlations. The kinematics chosen in the calculations is relevant for recent experiments at NIKHEF and Mainz.Comment: 17 pages, LaTeX, 9 figures include

How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Projected Linear Response Theory for Charge-Exchange Excitations and Double Beta Decay

The projected random phase approximation (PRPA) for charge-exchange excitations is derived from the time-dependent variational principle. Explicit results for the unperturbed energies (including the self-energy corrections), the PRPA matrices, and the transition matrix elements are presented. The effect of the projection procedure on the two-neutrino $\beta\beta$ decay in $^{76}Ge$ is briefly discussed.Comment: 12 pages text (LaTex) and 1 figure upon request, to be published in Phys. Lett.

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Generalized seniority scheme in light Sn isotopes

The yrast generalized seniority states are compared with the corresponding shell model states for the case of the Sn isotopes $^{104-112}$Sn. For most of the cases the energies agree within 100 keV and the overlaps of the wave functions are greater than 0.7.Comment: 8 pages, revtex. Submitted to Phys. Rev.

Assessment of left ventricular ejection fraction in patients eligible for ICD therapy: Discrepancy between cardiac magnetic resonance imaging and 2D echocardiography

OBJECTIVE: Implantable cardioverter defibrillators (ICD) and cardiac resynchronisation therapy (CRT) have substantially improved the survival of patients with cardiomyopathy. Eligibility for this therapy requires a left ventricular ejection fraction (LVEF) <35 %. This is largely based on studies using echocardiography. Cardiac magnetic resonance imaging (CMR) is increasingly utilised for LVEF assessment, but several studies have shown differences between LVEF assessed by CMR and echocardiography. The present study compared LVEF assessment by CMR and echocardiography in a heart failure population and evaluated effects on eligibility for device therapy. METHODS: 152 patients (106 male, mean age 65.5 ± 9.9 years) referred for device therapy were included. During evaluation of eligibility they underwent both CMR and echocardiographic LVEF assessment. CMR volumes were computed from a stack of short-axis images. Echocardiographic volumes were computed using Simpson’s biplane method. RESULTS: The study population demonstrated an underestimation of end-diastolic volume (EDV) and end-systolic volume (ESV) by echocardiography of 71 ± 53 ml (mean ± SD) and 70 ± 49 ml, respectively. This resulted in an overestimation of LVEF of 6.6 ± 8.3 % by echocardiography compared with CMR (echocardiographic LVEF 31.5 ± 8.7 % and CMR LVEF 24.9 ± 9.6 %). 28 % of patients had opposing outcomes of eligibility for cardiac device therapy depending on the imaging modality used. CONCLUSION: We found EDV and ESV to be underestimated by echocardiography, and LVEF assessed by CMR to be significantly smaller than by echocardiography. Applying an LVEF cut-off value of 35 %, CMR would significantly increase the number of patients eligible for device implantation. Therefore, LVEF cut-off values might need reassessment when using CMR