Renormalization Effects in a Dilute Bose Gas

The low-density expansion for a homogeneous interacting Bose gas at zero temperature can be formulated as an expansion in powers of $\sqrt{\rho a^3}$, where $\rho$ is the number density and $a$ is the S-wave scattering length. Logarithms of $\rho a^3$ appear in the coefficients of the expansion. We show that these logarithms are determined by the renormalization properties of the effective field theory that describes the scattering of atoms at zero density. The leading logarithm is determined by the renormalization of the pointlike $3 \to 3$ scattering amplitude.Comment: 10 pages, 1 postscript figure, LaTe

Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to nonassociativity. Our reflections keep wandering back to the $Brahmagupta$ $Fibonacc$ two square identity and then via the $Euler$ four square identity up to the $Degen$ $Ggraves$ $Cayley$ eight square identity. These glimpses of history incline and invite us to retell the story on how about one month after quaternions have been carved on the $Broughamian$ bridge octonions were discovered by $John$ $Thomas$ $Ggraves$, jurist and mathematician, a friend of $William$ $Rowan$ $Hamilton$. As for today we just mention en passant quaternionic and octonionic quantum mechanics, generalization of $Cauchy$ $Riemann$ equations for octonions and triality principle and $G_2$ group in spinor language in a descriptive way in order not to daunt non specialists. Relation to finite geometries is recalled and the links to the 7stones of seven sphere, seven imaginary octonions units in out of the $Plato$ cave reality applications are appointed . This way we are welcomed back to primary ideas of $Heisenberg$, $Wheeler$ and other distinguished fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure

Coherent states for exactly solvable potentials

A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier developed ones, including the oscillator based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum mechanical potential problems, like the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states, show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.Comment: 11 pages, 4 eps figures, uses graphicx packag

An approach to construct wave packets with complete classical-quantum correspondence in non-relativistic quantum mechanics

We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics to quantify this correspondence and show that the resulting Bohmian trajectories are also in a complete agreement with their classical counterparts.Comment: 15 pages, 13 figures, to appear in International Journal of Theoretical Physic

Precision Betacarotene Supplementation Enhanced Ovarian Function and the LH Release Pattern in Yearling Crossbred Anestrous Goats

The possible out-of-season effect of beta-carotene supplementation on ovulation rate (OR), antral follicles (AFN), and total ovarian activity (TOA = OR + AFN) as related to the LH release pattern in yearling anestrous goats was evaluated. In late April, Alpine-Saanen-Nubian x Criollo goats (n = 22, 26 N) were randomly allotted to: (1) Beta-carotene (BETA; n = 10, orally supplemented with 50 mg/goat/d; 36.4 ± 1.07 kg live weight (LW), 3.5 ± 0.20 units, body condition score (BCS) or (2) Non-supplemented (CONT; n = 12, 35.2 ± 1.07 kg LW, 3.4 ± 0.2 units BCS). Upon estrus synchronization, an intensive blood sampling (6 h × 15 min) was accomplished in May for LH quantifications; response variables included (pulsatility-PULSE, time to first pulse-TTFP, amplitude-AMPL, nadir-NAD and area under the curve-AUC). Thereafter, an ultrasonography scanning was completed to assess OR and AFN. The Munro algorithm was used to quantify LH pulsatility; if significant effects of time, treatment or interaction were identified, data were compared across time. Neither LW nor BCS (p > 0.05) or even the LH (p > 0.05); PULSE (4.1 ± 0.9 pulses/6 h), NAD (0.47 ± 0.13 ng) and AUC (51.7 ± 18.6 units) differed between treatments. Nonetheless, OR (1.57 vs. 0.87 ± 0.18 units) and TOA (3.44 vs. 1.87 ± 0.45 units) escorted by a reduced TTFP (33 vs. 126 ± 31.9 min) and an increased AMPL (0.55 vs. 0.24 ± 0.9 ng), favored to the BETA supplemented group (p < 0.05), possibly through a GnRH-LH enhanced pathway and(or) a direct effect at ovarian level. Results are relevant to speed-up the out-of-season reproductive outcomes in goats while may embrace translational applications

Goats as Valuable Animal Model to Test the Targeted Glutamate Supplementation upon Antral Follicle Number, Ovulation Rate, and LH-Pulsatility

The potential effect of intravenous administration of glutamate on the ovarian activity and the LH secretion pattern, considering the anestrous yearling goat as an animal model, were assessed. In late April, yearling goats (n = 20) were randomly assigned to either (1) Glutamate supplemented (GLUT; n = 10, Live Weight (LW) = 29.6 ± 1.02 kg, Body Condition (BCS) = 3.4 ± 0.2 units; i.v. supplemented with 7 mg GLUT kg−1 LW) or (2) Non-supplemented (CONT; n = 10; LW = 29.2 ± 1.07 kg, BCS = 3.5 ± 0.2 units; i.v. saline). The oats were estrus-synchronized; blood sampling (6 h × 15 min) was carried out for LH quantification. Response variables included pulsatility (PULSE), time to first pulse (TTFP), amplitude (AMPL), nadir (NAD), and area under the curve (AUC) of LH. Ovaries were ultra-sonographically scanned to assess ovulation rate (OR), number of antral follicles (AF), and total ovarian activity (TOA = OR + AF). LH-PULSE was quantified with the Munro algorithm; significant treatment x time interactions were evaluated across time. The variables LW and BCS did not differ (p > 0.05) between the experimental groups. Nevertheless, OR (1.77 vs. 0.87 ± 0.20 units), TOA (4.11 vs. 1.87 ± 0.47 units) and LH-PULSE (5.0 vs. 2.2 pulses 6 h-1) favored (p < 0.05) to the GLUT group. Our results reveal that targeted glutamate supplementation, the main central nervous system neurotransmitter, arose as an interesting strategy to enhance the hypothalamic–hypophyseal–ovarian response considering the anestrous-yearling goat as an animal model, with thought-provoking while promising translational applications

Unfolding of differential energy spectra in the MAGIC experiment

The paper describes the different methods, used in the MAGIC experiment, to unfold experimental energy distributions of cosmic ray particles (gamma-rays). Questions and problems related to the unfolding are discussed. Various procedures are proposed which can help to make the unfolding robust and reliable. The different methods and procedures are implemented in the MAGIC software and are used in most of the analyses.Comment: Submitted to NIM

Implementation of the Random Forest Method for the Imaging Atmospheric Cherenkov Telescope MAGIC

The paper describes an application of the tree classification method Random Forest (RF), as used in the analysis of data from the ground-based gamma telescope MAGIC. In such telescopes, cosmic gamma-rays are observed and have to be discriminated against a dominating background of hadronic cosmic-ray particles. We describe the application of RF for this gamma/hadron separation. The RF method often shows superior performance in comparison with traditional semi-empirical techniques. Critical issues of the method and its implementation are discussed. An application of the RF method for estimation of a continuous parameter from related variables, rather than discrete classes, is also discussed.Comment: 16 pages, 8 figure

Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope

We analyze the timing of photons observed by the MAGIC telescope during a flare of the active galactic nucleus Mkn 501 for a possible correlation with energy, as suggested by some models of quantum gravity (QG), which predict a vacuum refractive index \simeq 1 + (E/M_{QGn})^n, n = 1,2. Parametrizing the delay between gamma-rays of different energies as \Delta t =\pm\tau_l E or \Delta t =\pm\tau_q E^2, we find \tau_l=(0.030\pm0.012) s/GeV at the 2.5-sigma level, and \tau_q=(3.71\pm2.57)x10^{-6} s/GeV^2, respectively. We use these results to establish lower limits M_{QG1} > 0.21x10^{18} GeV and M_{QG2} > 0.26x10^{11} GeV at the 95% C.L. Monte Carlo studies confirm the MAGIC sensitivity to propagation effects at these levels. Thermal plasma effects in the source are negligible, but we cannot exclude the importance of some other source effect.Comment: 12 pages, 3 figures, Phys. Lett. B, reflects published versio