Shrinking the period lengths of continued fractions while still capturing convergents

Here we prove that every real quadratic irrational α can be expressed as a periodic non-simple continued fraction having period length one. Moreover, we show that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of α. We close with an application relating the structure of a quadratic α to its conjugate.     

The different effect of electron-electron interaction on the spectrum of atoms and quantum dots

Though atoms and quantum dots typically contain a comparable number of electrons, the number of discrete levels resolved in spectroscopy experiments is very different for the two systems. In atoms, hundreds of levels are observed while in quantum dots that number is usually smaller than 10. In the present work, this difference is traced to the different confining potentials in these systems. In atoms, the soft confining potential leads to large spatial extent of the excited electron's wave function and hence to weak Coulomb interaction with the rest of the atomic electrons. The resulting level broadening is smaller than the single particle level spacing and decreases as the excitation energy is increased. In quantum dots, on the other hand, the sharp confining potential results in electron-electron scattering rates that grow rapidly with energy and fairly quickly exceed the approximately constant single particle level spacing. The number of discrete levels in quantum dots is hence limited by electron-electron interaction, whose effect is negligible in atoms. Received 3 April 2000 and Received in final form 7 August 2000     

Dynamical crossover in an Ising spin glass above T(g): a muon-spin-relaxation investigation of Fe0.05TiS2

We investigate the temperature dependence of the spin-spin dynamical autocorrelation function of the Ising spin glass Fe0.05TiS2 through field dependent muon-spin lattice relaxation measurements. We successfully analyze the results using the Ogielski function, namely, t(-x)exp((-[t/tau](y)) as employed in numerical simulations. The experimental estimates of x, y, and tau are compared with those from simulations. Our major finding is that in this system the correlation function changes its nature from Ogielski to a form indistinguishable from pure stretched exponential upon cooling close to T(g), indicating a dynamical crossover.     

Microscopics of complexation between long DNA molecules and positively charged colloids

Extensive atomic force and electron microscopy reveal a new, generic DNA-colloid complex with a fixed number of DNA bases per colloid. The fiber shaped complex is stable in the presence of excess colloids in the solution. As more DNA is added to the solution and the ratio between colloids and DNA approaches the fiber's stoichiometry, the system undergoes a sharp coagulation transition. The system is restabilized at even higher DNA concentrations through localization of small colloid clusters on extensive DNA networks.     

Charge correlation in near-side hadron—Hadron jets at √s NN =200 GeV in PHENIX

We analyze the relative azimuthal (Δ?) distribution of same-charge and opposite-charge particle pairs. We then remove elliptic flow background using the ZYAM method. Comparisons between near angle Δ? peak widths are presented for various centralities.     

Search for magnetic order in undoped and doped spin‐gap systems by μSR

We introduce our μSR investigations of spin‐gap systems, such as, (1) a 2‐leg spin‐ladder material SrCu₂O₃, (2) a Haldane material (S=1 spin‐chain) Y₂BaNiO₅, (3) a spin‐Peierls material CuGeO₃, (4) a spin‐chain# material Sr₆Ca₈Cu₂₄O₄₁. All of these antiferromagnetic spin systems are characterized by a spin‐gap between the singlet ground‐state and the triplet first excited states. In the above‐mentioned materials, we confirmed the absence of magnetic order down to milli‐Kelvin regime, supporting the non‐magnetic feature of the ground‐state. If a spin‐gap system is doped with charges and/or vacancies at the spin site, unpaired spins are induced out of the singlet ground‐state. In some materials, doping completely destroys the singlet ground‐state and induces a bulk magnetic order. We report μSR investigations of doped materials as well, which clarifies the existence/absence of a magnetic order upon doping. This revised version was published online in July 2006 with corrections to the Cover Date.     

The role of CO in CO2 lasers

The population inversion in a CO₂-He glow discharge has been calculated, taking into account CO produced by dissociation in the discharge. The calculation was based on experimentally determined electron energy distributions and the measured effective relaxation constant of CO₂ (001). It is shown that the population inversion is negligible in the absence of CO.     

Dynamic spin relaxation processes of μ+ in an antiferromagnet

A new mechanism for positive muon spin-lattice relaxation (SLR) in an antiferromagnet is described. The temperature dependence of the relaxation rate (1/T ₁) is calculated in a simplified case, and SLR of muon in MnF₂ is studied in the context of this model.The author wishes to thank: S. R. Kreitzman and J. Shaham for their encouragement and stimulating ideas; L. P. Le, G. M. Luke, W. D. Wu, and Y. J. Uemura for helpful discussions.     

Ga NMR study of the local susceptibility in Kagome-based SrCr8Ga4O19: pseudogap and paramagnetic defects

We present the first Ga(4f ) NMR study of the Cr susceptibility in the archetype of kagome-based frustrated antiferromagnets, SrCr8Ga4O19. Our major finding is that the susceptibility of the frustrated lattice goes through a maximum around 50 K. Our data also support the existence of paramagnetic "clusters" of spins, responsible for the Curie behavior observed in the macroscopic susceptibility at low T. These results set novel features for the constantly debated physics of geometrically frustrated magnets.     

Magnetic dilution in the geometrically frustrated SrCr(9p)Ga(12-9p)O19 and the role of local dynamics: A muon spin relaxation study

We investigate the spin dynamics of SrCr(9p)Ga(12-9p)O19 for p below and above the percolation threshold p(c) using muon spin relaxation. Our major findings are as follows: (i) At T-->0 the relaxation rate is T independent and approximately p(3), (ii) the slowing down of spin fluctuation is activated with an energy U, which is also a linear function of p(3) and lim U as p-->0 = 8 K; this energy scale could stem only from a single ion anisotropy, and (iii) the p dependence of the dynamical properties is identical below and above p(c), indicating that they are controlled by local excitation.