Majorana solutions to the two-electron problem

A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable, contributions to the ground state energy of an atom with given Z coming also from any other Z. Instead, contributions relevant mainly for pedagogical reasons count simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as a simple alternative to Hylleraas' method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure

Utility of TERT Promoter Mutations for Cutaneous Primary Melanoma Diagnosis

Telomerase reverse transcriptase (TERT) promoter mutations are commonly found in malignant melanomas but rare in melanocytic nevi. To assess its potential diagnostic utility for the distinction of melanoma from nevus, we determined the TERT promoter mutation status of 86 primary melanomas, 72 melanocytic nevi, and 40 diagnostically problematic melanocytic proliferations. Of the 86 melanomas, 67 (77.9%) were TERT-positive, defined as harboring a hotspot TERT promoter mutation at positions -124C>T, -124_125CC>TT, -138_139CC>TT, or -146C>T. Of the 72 nevi, only 1 (1.4%) was TERT-positive. Of the 40 diagnostically uncertain melanocytic proliferations, 2 (5.0%) were TERT-positive. TERT positivity as a test for melanoma versus nevus had an accuracy of 87.3% [95% confidence interval (CI), 81.1-92.1], a sensitivity of 77.9% (95% CI, 68.9-85.4), a specificity of 98.6% (95% CI, 95.8-100), a positive predictive value of 98.5% (95% CI, 95.6-100), and a negative predictive value of 78.9% (95% CI, 72.6-85.4). Our results indicate that hotspot TERT promoter mutation status may be a useful ancillary parameter for the diagnosis of melanoma. In particular, the high specificity of these mutations for melanoma indicates the presence of a TERT promoter mutation in a melanocytic neoplasm associated with diagnostic controversy, or uncertainty should increase concern for a melanoma

Searching for the Slater Transition in the Pyrochlore Cd2_{2}Os2_{2}O7_{7} with Infrared Spectroscopy

Infrared reflectance measurements were made on the single crystal pyrochlore Cd$_{2}$Os$_{2}$O$_{7}$ in order to examine the transformations of the electronic structure and crystal lattice across the boundary of the metal insulator transition at $T_{MIT}=226K$. All predicted IR active phonons are observed in the conductivity over all temperatures and the oscillator strength is found to be temperature independent. These results indicate that charge ordering plays only a minor role in the MIT and that the transition is strictly electronic in nature. The conductivity shows the clear opening of a gap with $2\Delta=5.2k_{B}T_{MIT}$. The gap opens continuously, with a temperature dependence similar to that of BCS superconductors, and the gap edge having a distinct $\sigma(\omega)\thicksim\omega^{1/2}$ dependence. All of these observables support the suggestion of a Slater transition in Cd$_{2}$Os$_{2}$O$_{7}$.Comment: 4 pages, 4 figure

Identification of a Robust Methylation Classifier for Cutaneous Melanoma Diagnosis

Early diagnosis improves melanoma survival, yet the histopathological diagnosis of cutaneous primary melanoma can be challenging, even for expert dermatopathologists. Analysis of epigenetic alterations, such as DNA methylation, that occur in melanoma can aid in its early diagnosis. Using a genome-wide methylation screening, we assessed CpG methylation in a diverse set of 89 primary invasive melanomas, 73 nevi, and 41 melanocytic proliferations of uncertain malignant potential, classified based on interobserver review by dermatopathologists. Melanomas and nevi were split into training and validation sets. Predictive modeling in the training set using ElasticNet identified a 40-CpG classifier distinguishing 60 melanomas from 48 nevi. High diagnostic accuracy (area under the receiver operator characteristic curve = 0.996, sensitivity = 96.6%, and specificity = 100.0%)was independently confirmed in the validation set (29 melanomas, 25 nevi)and other published sample sets. The 40-CpG melanoma classifier included homeobox transcription factors and genes with roles in stem cell pluripotency or the nervous system. Application of the 40-CpG melanoma classifier to the diagnostically uncertain samples assigned melanoma or nevus status, potentially offering a diagnostic tool to assist dermatopathologists. In summary, the robust, accurate 40-CpG melanoma classifier offers a promising assay for improving primary melanoma diagnosis

Anisotropic Superexchange for nearest and next nearest coppers in chain, ladder and lamellar cuprates

We present a detailed calculation of the magnetic couplings between nearest-neighbor and next-nearest-neighbor coppers in the edge-sharing geometry, ubiquitous in many cuprates. In this geometry, the interaction between nearest neighbor coppers is mediated via two oxygens, and the Cu-O-Cu angle is close to 90 degrees. The derivation is based on a perturbation expansion of a general Hubbard Hamiltonian, and produces numerical estimates for the various magnetic energies. In particular we find the dependence of the anisotropy energies on the angular deviation away from the 90 degrees geometry of the Cu-O-Cu bonds. Our results are required for the correct analysis of the magnetic structure of various chain, ladder and lamellar cuprates.Comment: 13 pages, Latex, 7 figure

Uhlmann's geometric phase in presence of isotropic decoherence

Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly with increasing decoherence rate and that it is most fragile to weak decoherence for pure or nearly pure initial states. In the unitary case, we compare Uhlmann's geometric phase for mixed states with that occurring in standard Mach-Zehnder interferometry [Phys. Rev. Lett. {\bf 85}, 2845 (2000)] and show that the latter is more robust to reduction in the length of the Bloch vector. We also describe how Uhlmann's geometric phase in the present case could in principle be realized experimentally.Comment: New ref added, refs updated, journal ref adde

Theory of band gap bowing of disordered substitutional II-VI and III-V semiconductor alloys

For a wide class of technologically relevant compound III-V and II-VI semiconductor materials AC and BC mixed crystals (alloys) of the type A(x)B(1-x)C can be realized. As the electronic properties like the bulk band gap vary continuously with x, any band gap in between that of the pure AC and BC systems can be obtained by choosing the appropriate concentration x, granted that the respective ratio is miscible and thermodynamically stable. In most cases the band gap does not vary linearly with x, but a pronounced bowing behavior as a function of the concentration is observed. In this paper we show that the electronic properties of such A(x)B(1-x)C semiconductors and, in particular, the band gap bowing can well be described and understood starting from empirical tight binding models for the pure AC and BC systems. The electronic properties of the A(x)B(1-x)C system can be described by choosing the tight-binding parameters of the AC or BC system with probabilities x and 1-x, respectively. We demonstrate this by exact diagonalization of finite but large supercells and by means of calculations within the established coherent potential approximation (CPA). We apply this treatment to the II-VI system Cd(x)Zn(1-x)Se, to the III-V system In(x)Ga(1-x)As and to the III-nitride system Ga(x)Al(1-x)N.Comment: 14 pages, 10 figure

On the K^+D Interaction at Low Energies

The Kd reactions are considered in the impulse approximation with NN final-state interactions (NN FSI) taken into account. The realistic parameters for the KN phase shifts are used. The "quasi-elastic" energy region, in which the elementary KN interaction is predominantly elastic, is considered. The theoretical predictions are compared with the data on the K^+d->K^+pn, K^+d->K^0pp, K^+d->K^+d and K^+d total cross sections. The NN FSI effect in the reaction K^+d->K^+pn has been found to be large. The predictions for the Kd cross sections are also given for slow kaons, produced from phi(1020) decays, as the functions of the isoscalar KN scattering length a_0. These predictions can be used to extract the value of a_0 from the data.Comment: 22 pages, 5 figure

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

A New Faint Milky Way Satellite Discovered in the Pan-STARRS1 3π Survey

We present the discovery of a faint Milky Way satellite, Laevens 2/Triangulum II, found in the Panoramic Survey Telescope And Rapid Response System (Pan-STARRS 1) 3 pi imaging data and confirmed with follow-up wide-field photometry from the Large Binocular Cameras. The stellar system, with an absolute magnitude of M_V=-1.8 +/-0.5, a heliocentric distance of 30 +2/-2 kpc, and a half-mass radius of 34 +9/-8 pc, shows remarkable similarity to faint, nearby, small satellites such as Willman 1, Segue 1, Segue 2, and Bo\"otes II. The discovery of Laevens 2/Triangulum II further populates the region of parameter space for which the boundary between dwarf galaxies and globular clusters becomes tenuous. Follow-up spectroscopy will ultimately determine the nature of this new satellite, whose spatial location hints at a possible connection with the complex Triangulum-Andromeda stellar structures