Fractional Schr\"odinger equation and time dependent potentials

We investigate the solutions for a time dependent potential by considering two scenarios for the fractional Schr\"odinger equation. The first scenario analyzes the influence of the time dependent potential in the absence of the kinetic term. We obtain analytical and numerical solutions for this case by considering the Caputo fractional time derivative, which extends Rabi's model. In the second scenario, we incorporate the kinetic term in the Schr\"odinger equation and consider fractional spatial derivatives. For this case, we analyze the spreading of the Gaussian wave package under the action of the time and spatial fractional differential operators

Some Properties of R\'{e}nyi Entropy over Countably Infinite Alphabets

In this paper we study certain properties of R\'{e}nyi entropy functionals $H_\alpha(\mathcal{P})$ on the space of probability distributions over $\mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties shown parallel those known in the finite alphabet case, while others illustrate a quite different behaviour of R\'enyi entropy in the infinite case. In particular, it is shown that, for any distribution $\mathcal P$ and any $r\in[0,\infty]$, there exists a sequence of distributions $\mathcal{P}_n$ converging to $\mathcal{P}$ with respect to the total variation distance, such that $\lim_{n\to\infty}\lim_{\alpha\to{1+}} H_\alpha(\mathcal{P}_n) = \lim_{\alpha\to{1+}}\lim_{n\to\infty} H_\alpha(\mathcal{P}_n) + r$.Comment: 13 pages (single-column

Measurement of high-p_T Single Electrons from Heavy-Flavor Decays in p+p Collisions at sqrt(s) = 200 GeV

The momentum distribution of electrons from decays of heavy flavor (charm and beauty) for midrapidity |y| < 0.35 in p+p collisions at sqrt(s) = 200 GeV has been measured by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) over the transverse momentum range 0.3 < p_T < 9 GeV/c. Two independent methods have been used to determine the heavy flavor yields, and the results are in good agreement with each other. A fixed-order-plus-next-to-leading-log pQCD calculation agrees with the data within the theoretical and experimental uncertainties, with the data/theory ratio of 1.72 +/- 0.02^stat +/- 0.19^sys for 0.3 < p_T < 9 GeV/c. The total charm production cross section at this energy has also been deduced to be sigma_(c c^bar) = 567 +/- 57^stat +/- 224^sys micro barns.Comment: 375 authors from 57 institutions, 6 pages, 3 figures. Submitted to Physical Review Letters. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Measurement of prompt J/ψ pair production in pp collisions at √s = 7 Tev

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Observation of the diphoton decay of the Higgs boson and measurement of its properties

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Search for neutral MSSM Higgs bosons decaying to a pair of tau leptons in pp collisions

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Measurement of top quark–antiquark pair production in association with a W or Z boson in pp collisions at √s=8 TeV

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Searches for electroweak production of charginos, neutralinos, and sleptons decaying to leptons and W, Z, and Higgs bosons in pp collisions at 8 TeV

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