S-duality and the N=2 Lens Space Index

We discuss some of the analytic properties of lens space indices for 4d N=2 theories of class S. The S-duality properties of these theories highly constrain the lens space indices, and imply in particular that they are naturally acted upon by a set of commuting difference operators corresponding to surface defects. We explicitly identify the difference operators to be a matrix-valued generalization of the elliptic Ruijsenaars-Schneider model. In a special limit these difference operators can be expressed naturally in terms of Cherednik operators appearing in the double affine Hecke algebras, with the eigenfunctions given by non-symmetric Macdonald polynomials.Comment: 33 pages, 3 figures, harvmac. v2: minor correction

Quantum gate using qubit states separated by terahertz

A two-qubit quantum gate is realized using electronic excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase locked lasers are used to excite a stimulated Raman transition between two metastable states $D_{3/2}$ and $D_{5/2}$ separated by 1.82 THz in a single trapped $^{40}$Ca$^+$ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.Comment: 4 pages, 4 figure

How do Neutrinos Propagate ? - Wave-Packet Treatment of Neutrino Oscillation

The wave-packet treatment of neutrino oscillation developed previously is extended to the case in which momentum distribution functions are taken to be a Gaussian form with both central values and dispersions depending on the mass eigenstates of the neutrinos. It is shown among other things that the velocity of the neutrino wave packets does not in general agree with what one would expect classically and that relativistic neutrinos emitted from pions nevertheless do follow, to a good approximation, the classical trajectory.Comment: 13 page. No figure. Typeset using PTPTeX.st

Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at $k\simeq 10^{-2.5}$ Mpc$^{-1}$ with the upper limit $B\lesssim 3$ nG.Comment: 14 pages, 6 figure

Constraints on the Primordial Magnetic Field from σ8\sigma_8

A primordial magnetic field (PMF) can affect the evolution of density field fluctuations in the early universe.In this paper we constrain the PMF amplitude $B_\lambda$ and power spectral index $n_\mathrm{B}$ by comparing calculated density field fluctuations with observational data, i.e. the number density fluctuation of galaxies.We show that the observational constraints on cosmological density fluctuations, as parameterized by $\sigma_8$, lead to strong constraints on the amplitude and spectral index of the PMF.Comment: 11 pages, 1 figure, accepted for publication as Phys. Rev.

Theoretical Response to the Discovery of Deeply Bound Pionic States in 208Pb(d,3He) reactions

Recently, deeply bound pionic states were found experimentally in (d, $^3$He) reactions on $^{208}$Pb. They found an isolated peak structure in the bound region below the pion production threshold. We study theoretically these excitation functions in (d, $^3$He) reactions on $^{208}$Pb at T$_d$=600 MeV. We found very good agreement with the (d, $^3$He) excitation functions and could identify the underlying structures of the pionic states. We study the energy dependence of the (d, $^3$He) reactions and the change of the excitation functions with the incident energy.Comment: 5 pages, Latex, Figures available on request, Z.Phys.A.accepte

Search for CP-violation in Positronium Decay

CP-violation in the quark sector has been well established over the last decade, but has not been observed in the lepton sector. We search for CP-violating decay processes in positronium, using the angular correlation of (\vec{S}\cdot\vec{k_{1}})(\vec{S}\cdot\vec{k_{1}}\times\vec{k_{2}}), where \vec{S} is the the positronium spin and \vec{k_{1}}, \vec{k_{2}} are the directions of the positronium decay photons. To a sensitivity of 2.2\times10^{-3}, no CP-violation has been found, which is at the level of the CP-violation amplitude in the K meson. A 90% confidence interval of the CP-violation parameter (C_{CP}) was determined to be -0.0023 < C_{CP} < 0.0049. This result is a factor 7 more strict than that of the previous experiment

Nuclear Quadrupole Effects in Deeply Bound Pionic Atoms

We have studied nuclear quadrupole deformation effects in deeply bound pionic atoms theoretically. We have evaluated the level shifts and widths of the hyperfine components using the first order perturbation theory and compared them with the effects of neutron skin. We conclude that the nuclear quadrupole deformation effects for deeply bound $1s$ and $2p$ states are very difficult to observe and that the effects could be observed for $3d$ states. We also conclude that the deformation effects are sensitive to the parameters of the pion-nucleus optical potential.Comment: Latex 11pages, Figures available on reques