Time-resolved Kerr rotation spectroscopy under the radio frequency field to depolarize dynamic nuclear polarization reveals the intrinsic spin-relaxation time ͑T 2 ‫ء‬ ͒ and g factor of two-dimensional electrons in a quantum Hall system. Out-of-plane magnetic field increases the spin coherence drastically through the Landau level quantization. T 2 ‫ء‬ is enhanced strongly around odd filling factors where a quantum Hall ferromagnet is formed. Collapse of spin coherence and appearance of an anomalous Kerr signal observed around = 1 are discussed in the relation to the formation of Skyrmions.

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Abstract-Specific rain attenuation is discussed from the viewpoint of numerical solution for scattering and absorption of electromagnetic waves related to dielectric spheres. Special attention is paid to the quantitative evaluations considering the change of temperature and the existence of multiple scattering effect. The analysis is based on the set of Stratton's vector spherical wave functions and its addition theorem, which lead to the simultaneous linear equations for the expansion coefficients with adaptively selected truncation numbers. Computed extinction cross sections lead directly to the specific rain attenuation, where the Weibull raindrop distribution model is used. It is discussed how the dependence of the permittivity of water on temperature and frequency affects the attenuation property. Furthermore, the effect of multiple scattering is evaluated in terms of the root mean square of attenuation deviation from the simple superposition of single scattering (Mie's) coefficients. Contrary to general belief, this deviation is the highest at around the boundary between microwave and millimeter wave bands.

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The dynamics between electron and nuclear spins in quantum Hall regime is investigated by a time-resolved Kerr rotation (TRKR) spectroscopy carried down in tilted-field geometry. The spin-flip energy varies almost linearly with the applied magnetic field under the nuclear spin depolarizing radio frequency field and the helicity modulation of circularly polarized pump, while the spin-flip energy obtained under a circularly polarized pump deviates from linearly behavior. This deviation is ascribed to the Overhauser shift due to dynamic nuclear spin polarization (DNP). The DNP depends markedly on the filling factor and present peaks at even filling factors. These results can be well explained by a simple model based on the detailed balance between electron and nuclear spins.

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The present paper numerically clarifies the degree of multiple scattering effects, which has been believed to become significant at high frequencies more than several hundred gigahertz. The specific rain attenuation is evaluated directly from an extinction cross section of dielectric spheres. A set of small dielectric spheres are randomly allocated inside a big fictitious sphere by using Weibull raindrop size distribution model. In order to take account of the multiple scattering among raindrops, we employ the mode matching method based on vector spherical wave functions and its addition theorem. Numerical results are demonstrated for the root mean square deviation of the specific attenuation between the cases with and without multiple scattering terms. Contrary to general belief, the deviation is the highest at around the boundary between microwave and millimeter wave bands.

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