Derivative dispersion relations above the physical threshold

We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical interest as forward scattering amplitudes, this replacement can be analytically performed, leading to novel Extended Derivative Dispersion Relations (EDDR), which, in principle, are valid for any energy above the physical threshold. We then verify the equivalence between the IDR and EDDR by means of a popular parametrization for total cross sections from proton-proton and antiproton-proton scattering and compare the results with those obtained through other representations for the derivative relations. Critical aspects on the limitations of the whole analysis, from both formal and practical points of view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358 (2007

Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2 e2∕ h conductance quantisation, even where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of various transport experiments in terms of Majorana zero modes. Here we show that the Andreev versus Majorana controversy is clarified when framed in the language of non-Hermitian topology, the natural description for quantum systems open to the environment. This change of paradigm allows one to understand topological transitions and the emergence of zero modes in more general systems than can be described by band topology. This is achieved by studying exceptional point bifurcations in the complex spectrum of the system’s non-Hermitian Hamiltonian. Within this broader topological classification, Majoranas from both conventional band topology and a large subset of Andreev levels at zero energy are in fact topologically equivalent, which explains why they cannot be distinguishedWe thank J. Cayao for useful discussions in the early stages of this work. Research supported by the Spanish Ministry of Science, Innovation and Universities through Grants PGC2018-097018-B-I00, FIS2015-65706-P, FIS2015-64654-P, FIS2016-80434-P (AEI/FEDER, EU), the FPI programme BES-2016-078122, the Ramón y Cajal programme Grants RYC-2011-09345, RYC-2013-14645, the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), and the European Union’s Horizon 2020 research and innovation programme under the FETOPEN Grant Agreement No. 828948. We also acknowledge support from CSIC Research Platform on Quantum Technologies PTI-00

Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators

We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrodinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Holder continuity near almost reducible energies (an essential support of absolutely continuous spectrum). For non-perturbatively small potentials (and for the almost Mathieu operator with subcritical coupling), our results apply for all energies.Comment: 16 page

Optical Turbulence Measurements and Models for Mount John University Observatory

Site measurements were collected at Mount John University Observatory in 2005 and 2007 using a purpose-built scintillation detection and ranging system. $C_n^2(h)$ profiling indicates a weak layer located at 12 - 14 km above sea level and strong low altitude turbulence extending up to 5 km. During calm weather conditions, an additional layer was detected at 6 - 8 km above sea level. $V(h)$ profiling suggests that tropopause layer velocities are nominally 12 - 30 m/s, and near-ground velocities range between 2 -- 20 m/s, dependent on weather. Little seasonal variation was detected in either $C_n^2(h)$ and $V(h)$ profiles. The average coherence length, $r_0$, was found to be $7 \pm 1$ cm for the full profile at a wavelength of 589 nm. The average isoplanatic angle, $\theta_0$, was $1.0 \pm 0.1$ arcsec. The mean turbulence altitude, $\bar{h_0}$, was found to be $2.0\pm0.7$ km above sea level. No average in the Greenwood frequency, $f_G$, could be established due to the gaps present in the \vw\s profiles obtained. A modified Hufnagel-Valley model was developed to describe the $C_n^2(h)$ profiles at Mount John, which estimates $r_0$ at 6 cm and $\theta_0$ at 0.9 arcsec. A series of $V(h)$ models were developed, based on the Greenwood wind model with an additional peak located at low altitudes. Using the $C_n^2(h)$ model and the suggested $V(h)$ model for moderate ground wind speeds, $f_G$ is estimated at 79 Hz.Comment: 14 pages; accepted for publication in PAS

The HIHI- and H2H_{2}-to-stellar mass correlations of late- and early-type galaxies and their consistency with the observational mass functions

We compile and carrefully homogenize local galaxy samples with available information on stellar, $\rm HI$ and/or $\rm H_{2}$ masses, and morphology. After processing the information on upper limits in the case of non gas detections, we determine the $\rm HI$- and $\rm H_{2}$-to-stellar mass relations and their $1\sigma$ scatter for both late- and early-type galaxies. The obtained relations are fitted to single or double power laws. Late-type galaxies are significantly gas richer than early-type ones, specially at high masses. The respective $\rm H_{2}$-to-$\rm HI$ mass ratios as a function of $M_{\ast}$ are discussed. Further, we constrain the full mass-dependent distribution functions of the $\rm HI$- and $\rm H_{2}$-to-stellar mass ratios. We find that they can be described by a Schechter function for late types and a (broken) Schechter + uniform function for early types. By using the observed galaxy stellar mass function and the volume-complete late-to-early-type galaxy ratio as a function of $M_{\ast}$, these empirical distribution functions are mapped into $\rm HI$ and $\rm H_{2}$ mass functions. The obtained mass functions are consistent with those inferred from large surveys. The empirical gas-to-stellar mass relations and their distributions for local late- and early-type galaxies presented here can be used to constrain models and simulations of galaxy evolution.Comment: 43 pages, 18 figures, to appear in RMxAA. Minor corrections introduced. The presented results are optimal for comparisons with theoretical predictions. Py-code to generate the HI- and H2-to-stellar mass relations and their 1sigma scatter, as well as the full mass-dependent distribution functions of the MHI/Ms and MH2/Ms ratios are available upon request to A.R. Calett

The bivariate gas-stellar mass distributions and the mass functions of early- and late-type galaxies at z∼0z\sim0

We report the bivariate HI- and H$_2$-stellar mass distributions of local galaxies in addition of an inventory of galaxy mass functions, MFs, for HI, H$_2$, cold gas, and baryonic mass, separately into early- and late-type galaxies. The MFs are determined using the HI and H$_2$ conditional distributions and the galaxy stellar mass function, GSMF. For the conditional distributions we use the compilation presented in Calette et al. 2018. For determining the GSMF from $M_{\ast}\sim3\times10^{7}$ to $3\times10^{12}$ $M_{\odot}$, we combine two spectroscopic samples from the SDSS at the redshift range $0.0033<z<0.2$. We find that the low-mass end slope of the GSMF, after correcting from surface brightness incompleteness, is $\alpha\approx-1.4$, consistent with previous determinations. The obtained HI MFs agree with radio blind surveys. Similarly, the H$_2$ MFs are consistent with CO follow-up optically-selected samples. We estimate the impact of systematics due to mass-to-light ratios and find that our MFs are robust against systematic errors. We deconvolve our MFs from random errors to obtain the intrinsic MFs. Using the MFs, we calculate cosmic density parameters of all the baryonic components. Baryons locked inside galaxies represent 5.4% of the universal baryon content, while $\sim96$% of the HI and H$_2$ mass inside galaxies reside in late-type morphologies. Our results imply cosmic depletion times of H$_2$ and total neutral H in late-type galaxies of $\sim 1.3$ and 7.2 Gyr, respectively, which shows that late type galaxies are on average inefficient in converting H$_2$ into stars and in transforming HI gas into H$_2$. Our results provide a fully self-consistent empirical description of galaxy demographics in terms of the bivariate gas--stellar mass distribution and their projections, the MFs. This description is ideal to compare and/or to constrain galaxy formation models.Comment: 37 pages, 17 figures. Accepted for publication in PASA. A code that displays tables and figures with all the relevant statistical distributions and correlations discussed in this paper is available here https://github.com/arcalette/Python-code-to-generate-Rodriguez-Puebla-2020-result