On Close Relationship between Classical Time-Dependent Harmonic Oscillator and Non-Relativistic Quantum Mechanics in One Dimension

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\"odinger's equation. These results, with support from numerical simulations, strongly suggest that two uncoupled classical harmonic oscillators, which initially have a 90\degree relative phase shift and then are simultaneously disturbed by the same parametric perturbation of a finite duration, manifest behavior which can be mapped to that of a single quantum particle, with classical 'range relations' analogous to the uncertainty relations of quantum physics.Comment: 20 pages, 8 figures, 1 table, final versio

The Generalization of the Decomposition of Functions by Energy Operators

This work starts with the introduction of a family of differential energy operators. Energy operators ($Psi_R^+$, $Psi_R^-$) were defined together with a method to decompose the wave equation in a previous work. Here the energy operators are defined following the order of their derivatives ($Psi_k^+$, $Psi_k^-$, k = {0,1,2,..}). The main part of the work is to demonstrate that for any smooth real-valued function f in the Schwartz space ($S^-(R)$), the successive derivatives of the n-th power of f (n in Z and n not equal to 0) can be decomposed using only $Psi_k^+$ (Lemma) or with $Psi_k^+$, $Psi_k^-$ (k in Z) (Theorem) in a unique way (with more restrictive conditions). Some properties of the Kernel and the Image of the energy operators are given along with the development. Finally, the paper ends with the application to the energy function.Comment: The paper was accepted for publication at Acta Applicandae Mathematicae (15/05/2013) based on v3. v4 is very similar to v3 except that we modified slightly Definition 1 to make it more readable when showing the decomposition with the families of energy operator of the derivatives of the n-th power of

New Physics and CP Violation in Hyperon Nonleptonic Decays

The sum of the CP-violating asymmetries A(Lambda_-^0) and A(Xi_-^-) in hyperon nonleptonic decays is presently being measured by the E871 experiment. We evaluate contributions to the asymmetries induced by chromomagnetic-penguin operators, whose coefficients can be enhanced in certain models of new physics. Incorporating recent information on the strong phases in Xi->Lambda pi decay, we show that new-physics contributions to the two asymmetries can be comparable. We explore how the upcoming results of E871 may constrain the coefficients of the operators. We find that its preliminary measurement is already better than the epsilon parameter of K-Kbar mixing in bounding the parity-conserving contributions.Comment: 12 pages, 2 figure

CP Violation in Hyperon Nonleptonic Decays within the Standard Model

We calculate the CP-violating asymmetries A(Lambda_-^0) and A(Xi_-^-) in nonleptonic hyperon decay within the Standard Model using the framework of heavy-baryon chiral perturbation theory (chiPT). We identify those terms that correspond to previous calculations and discover several errors in the existing literature. We present a new result for the lowest-order (in chiPT) contribution of the penguin operator to these asymmetries, as well as an estimate for the uncertainty of our result that is based on the calculation of the leading nonanalytic corrections.Comment: 21 pages, 2 figures; discussion clarified, results & conclusions unchanged, to appear in Phys. Rev.

Cluster Masses Accounting for Structure along the Line of Sight

Weak gravitational lensing of background galaxies by foreground clusters offers an excellent opportunity to measure cluster masses directly without using gas as a probe. One source of noise which seems difficult to avoid is large scale structure along the line of sight. Here I show that, by using standard map-making techniques, one can minimize the deleterious effects of this noise. The resulting uncertainties on cluster masses are significantly smaller than when large scale structure is not properly accounted for, although still larger than if it was absent altogether.Comment: 5 pages, 5 figure

Modulation of the secretion of potassium by accompanying anions in humans

Modulation of the secretion of potassium by accompanying anions in humans. In animals, secretion of potassium (K) in the cortical collecting duct (CCD) is modulated by the properties of the accompanying anion. In humans, results are inconclusive as previous studies have not differentiated between a kaliuresis due to a rise in the concentration of K from one due to an increase in the volume of urine. Our purpose was to study the effects of chloride (Cl) and bicarbonate on the secretion of K in the CCD in humans using the transtubular K concentration gradient (TTKG), a semi-quantitative index of secretion of K in the terminal CCD. After control blood and urine samples were obtained, all subjects ingested 0.2mg fludrocortisone to ensure that mineralocorticoids were not limiting the secretion of K. The anionic composition of the urine was varied using three protocols: Normal subjects (N = 11) ingested cystine and methionine to induce sulfaturia; nine subjects with a contracted ECF volume (to lower the concentration of Cl in the urine) were also studied during sulfaturia following the ingestion of cystine and methionine; 13 normovolemic subjects were studied during bicarbonaturia following the ingestion of acetazolamide. When the concentration of Cl in the urine was > 15 mmol/liter, sulfate had no effect on the TTKG. With lower concentrations of Cl in the urine, the TTKG rose 1.5-fold. The TTKG rose 1.8-fold in the presence of bicarbonaturia despite concentrations of Cl in the urine that were >15 mmol/liter, suggesting that bicarbonate has additional effects on this K secretory process. At comparable concentrations of sulfate and bicarbonate in the urine, the TTKG was increased only with bicarbonaturia. We conclude that it is important to control for the effects of the accompanying anions when evaluating the role of the kidney in disorders of K homeostasis

Hadronic properties of the S_{11}(1535) studied by electroproduction off the deuteron

Properties of excited baryonic states are investigated in the context of electroproduction of baryon resonances off the deuteron. In particular, the hadronic radii and the compositeness of baryon resonances are studied for kinematic situations in which their hadronic reinteraction is the dominant contribution. Specifically, we study the reaction $d(e,e'S_{11})N$ at $Q^2\ge 1 GeV^2$ for kinematics in which the produced hadronic state reinteracts predominantly with the spectator nucleon. A comparison of constituent quark model and effective chiral Lagrangian calculations of the $S_{11}$ shows substantial sensitivity to the structure of the produced resonance.Comment: 24 pages, 5 figure

The decay pi0 to gamma gamma to next to leading order in Chiral Perturbation Theory

The two photon decay width of the neutral pion is analyzed within the combined framework of Chiral Perturbation Theory and the 1/Nc expansion up to order p^6 and p^4 times 1/Nc in the decay amplitude. The eta' is explicitly included in the analysis. It is found that the decay width is enhanced by about 4.5% due to the isospin-breaking induced mixing of the pure U(3) states. This effect, which is of leading order in the low energy expansion, is shown to persist nearly unchanged at next to leading order. The chief prediction for the width with its estimated uncertainty is 8.10+-0.08 eV. This prediction at the 1% level makes the upcomming precision measurement of the decay width even more urgent. Observations on the eta and eta' can also be made, especially about their mixing, which is shown to be significantly affected by next to leading order corrections.Comment: 21 pages, two figure

Consistency tests of AMPCALCULATOR and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial based approach

Ampcalculator is a Mathematica based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one-loop (upto $O(p^4)$) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling $G_{27}$. Another illustrative set of amplitudes at tree level we provide is in the context of $\tau$-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. Kaon-Compton amplitude has been checked and a minor error in published results has been pointed out. This exercise is a tutorial based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and used in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.Comment: 25 pages, plain latex, corresponds to version to appear in EPJA, additional ancillary files adde