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    Phase reduction of stochastic limit cycle oscillators

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    We point out that the phase reduction of stochastic limit cycle oscillators has been done incorrectly in the literature. We present a correct phase reduction method for oscillators driven by weak external white Gaussian noises. Numerical evidence demonstrates that the present phase equation properly approximates the dynamics of the original full oscillator system.Comment: 4 pages, 2 figure

    Orbital Properties of Sr3Ru2O7 and Related Ruthenates Probed by 17O-NMR

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    We report a site-separated 17^{17}O-NMR study of the layered perovskite ruthenate Sr3_3Ru2_2O7_7, which exhibits nearly two-dimensional transport properties and itinerant metamagnetism at low temperatures. The local hole occupancies and the spin densities in the oxygen 2p2p orbitals are obtained by means of tight-binding analyses of electric field gradients and anisotropic Knight shifts. These quantities are compared with two other layered perovskite ruthenates: the two-dimensional paramagnet Sr2_2RuO4_4 and the three-dimensional ferromagnet SrRuO3_3. The hole occupancies at the oxygen sites are very large, about one hole per ruthenium atom. This is due to the strong covalent character of the Ru-O bonding in this compound. The magnitude of the hole occupancy might be related to the rotation or tilt of the RuO6_6 octahedra. The spin densities at the oxygen sites are also large, 20-40% of the bulk susceptibilities, but in contrast to the hole occupancies, the spin densities strongly depend on the dimensionality. This result suggests that the density-of-states at the oxygen sites plays an essential role for the understanding of the complex magnetism found in the layered perovskite ruthenates.Comment: 9 pages, 5 figures, to be published in Phys. Rev.