Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.Comment: 62 pages, 1 figure. A slight extension of the published versio

High Educational Aspirations Among Pregnant Adolescents Are Related to Pregnancy Unwantedness and Subsequent Parenting Stress and Inadequacy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106966/1/jomf12103.pd

Optical Lattice Induced Light Shifts in an Yb Atomic Clock

We present an experimental study of the lattice induced light shifts on the 1S_0-3P_0 optical clock transition (v_clock~518 THz) in neutral ytterbium. The ``magic'' frequency, v_magic, for the 174Yb isotope was determined to be 394 799 475(35)MHz, which leads to a first order light shift uncertainty of 0.38 Hz on the 518 THz clock transition. Also investigated were the hyperpolarizability shifts due to the nearby 6s6p 3P_0 - 6s8p 3P_0, 6s8p 3P_2, and 6s5f 3F_2 two-photon resonances at 759.708 nm, 754.23 nm, and 764.95 nm respectively. By tuning the lattice frequency over the two-photon resonances and measuring the corresponding clock transition shifts, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 uK deep, lattice at the magic wavelength. In addition, we have confirmed that a circularly polarized lattice eliminates the J=0 - J=0 two-photon resonance. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10^-17.Comment: Accepted to PR

Frequency evaluation of the doubly forbidden 1S0→3P0^1S_0\to ^3P_0 transition in bosonic 174^{174}Yb

We report an uncertainty evaluation of an optical lattice clock based on the $^1S_0\leftrightarrow^3P_0$ transition in the bosonic isotope $^{174}$Yb by use of magnetically induced spectroscopy. The absolute frequency of the $^1S_0\leftrightarrow^3P_0$ transition has been determined through comparisons with optical and microwave standards at NIST. The weighted mean of the evaluations is $\nu$($^{174}$Yb)=518 294 025 309 217.8(0.9) Hz. The uncertainty due to systematic effects has been reduced to less than 0.8 Hz, which represents $1.5\times10^{-15}$ in fractional frequency.Comment: 4 pages, 3 figure -Submitted to PRA Rapid Communication

Motif-based communities in complex networks

Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman-Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks

On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular and honeycomb lattices, with both binary and Gaussian disorder distributions. For square and triangular lattices with binary disorder, the estimated position of the multicritical point is in numerical agreement with recent conjectures regarding its exact location. For the remaining four cases, our results indicate disagreement with the respective versions of the conjecture, though by very small amounts, never exceeding 0.2%. Our results for: (i) the correlation-length exponent $\nu$ governing the ferro-paramagnetic transition; (ii) the critical domain-wall energy amplitude $\eta$; (iii) the conformal anomaly $c$; (iv) the finite-size susceptibility exponent $\gamma/\nu$; and (v) the set of multifractal exponents $\{\eta_k \}$ associated to the moments of the probability distribution of spin-spin correlation functions at the multicritical point, are consistent with universality as regards lattice structure and disorder distribution, and in good agreement with existing estimates.Comment: RevTeX 4, 9 pages, 2 .eps figure