A Characterization of Locally Testable Affine-Invariant Properties via Decomposition Theorems

Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$ satisfies $\mathcal{P}$ and rejects when $f$ is "far" from satisfying $\mathcal{P}$. In this paper, we give a characterization of affine-invariant properties that are (two-sided error) testable with a constant number of queries. The characterization is stated in terms of decomposition theorems, which roughly claim that any function can be decomposed into a structured part that is a function of a constant number of polynomials, and a pseudo-random part whose Gowers norm is small. We first give an algorithm that tests whether the structured part of the input function has a specific form. Then we show that an affine-invariant property is testable with a constant number of queries if and only if it can be reduced to the problem of testing whether the structured part of the input function is close to one of a constant number of candidates.Comment: 27 pages, appearing in STOC 2014. arXiv admin note: text overlap with arXiv:1306.0649, arXiv:1212.3849 by other author

Dead cone due to parton virtuality

A general expression for the dead cone of gluons radiated by virtual partons has been derived. The conventional dead cone for massive on-shell quarks and the dead cone for the massless virtual partons have been obtained by using different limits of the general expression. Radiative suppression due to the virtuality of initial parton jets in Heavy-Ion Collisions (HIC) has been discussed. It is observed that the suppression caused by the high virtuality is overwhelmingly large as compared to that on account of conventional dead-cone of heavy quarks. The dead cone due to virtuality may play a crucial role in explaining the observed similar suppression patterns of light and heavy quarks jets in heavy ion collisions at Relativistic Heavy Ion Collider (RHIC)

Quantum integrability of bosonic Massive Thirring model in continuum

By using a variant of the quantum inverse scattering method, commutation relations between all elements of the quantum monodromy matrix of bosonic Massive Thirring (BMT) model are obtained. Using those relations, the quantum integrability of BMT model is established and the S-matrix of two-body scattering between the corresponding quasi particles has been obtained. It is observed that for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles that can form a quantum-soliton state of BMT model. We also calculate the binding energy for a N-soliton state of quantum BMT model.Comment: Latex, 23 pages, no figure

Derivation of upward muon energy spectra in the TeV range produced by neutrinos from 3C273 AGN and diffuse atmospheric sources

The neutrino-induced upward muon energy spectrum on Earth at the TeV energy range emitted by the point source 3C273 AGN has been calculated using the AGN-emitted neutrino spectrum of Szabo and Protheroe and the result has been compared with that expected from background neutrinos. The QCD-based model of Berezinsky et al. has been fairly employed to estimate the muon contribution due to the charge current interactions in rock. The diffuse neutrino-induced upward muon energy spectrum from AGN sources has also been estimated and compared with the expected results from the spectra of prompt neutrinos and atmospheric backgrounds. It is found that the upward muon fluxes generated by AGN neutrinos are dominating the Universe beyond 10 TeV muon energy

μ\muSR and Neutron Diffraction Investigations on Reentrant Ferromagnetic Superconductor Eu(Fe{0.86}Ir{0.14})2As2

Results of muon spin relaxation ($\mu$SR) and neutron powder diffraction measurements on a reentrant superconductor Eu(Fe$_{0.86}$Ir$_{0.14}$)$_2$As$_2$ are presented. Eu(Fe$_{0.86}$Ir$_{0.14}$)$_2$As$_2$ exhibits superconductivity at $T_{\rm c\,on} \approx 22.5$~K competing with long range ordered Eu$^{+2}$ moments below $\approx 18$ K. A reentrant behavior (manifested by nonzero resistivity in the temperature range 10--17.5 K) results from an exquisite competition between the superconductivity and magnetic order. The zero field $\mu$SR data confirm the long range magnetic ordering below $T_{\rm Eu} = 18.7(2)$ K. The transition temperature is found to increase with increasing magnetic field in longitudinal field $\mu$SR which along with the neutron diffraction results, suggests the transition to be ferromagnetic. The neutron diffraction data reveal a clear presence of magnetic Bragg peaks below $T_{\rm Eu}$ which could be indexed with propagation vector k = (0, 0, 0), confirming a long range magnetic ordering in agreement with $\mu$SR data. Our analysis of the magnetic structure reveals an ordered magnetic moment of $6.29(5)\,\mu_{\rm B}$ (at 1.8 K) on the Eu atoms and they form a ferromagnetic structure with moments aligned along the $c$-axis. No change in the magnetic structure is observed in the reentrant or superconducting phases and the magnetic structure remains same for 1.8 K $\leq T \leq T_{\rm Eu}$. No clear evidence of structural transition or Fe moment ordering was found.Comment: 9 pages, 7 figures, to appear in Phys. Rev.