Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry

Negative magnetoresistance in indium antimonide whiskers doped with tin

Negative magnetoresistance of InSb whiskers with different impurity concentrations 4.4 × 10 ¹⁶–7.16 × 10 ¹⁷ cm −³ was studied in longitudinal magnetic field 0–14 T in the temperature range 4.2–77 K. The negative magnetoresistance reaches about 50% for InSb whiskers with impurity concentration in the vicinity to the metal–insulator transition. The negative magnetoresistance decreases to 35 and 25% for crystals with Sn concentration from the metal and dielectric side of the transition. The longitudinal magnetoresistance twice crosses the axis of the magnetic field induction for the lightly doped crystals. The behavior of the negative magnetoresistance could be explained by the existence of classical size effect, in particular boundary scattering in the subsurface whisker layer

Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation

We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), additionally to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its principal dynamical characteristic is that, typically, it develops over much larger times than the modulational instability, a feature that is qualitatively justified by comparison of the corresponding instability growth rates

Импедансная спектроскопия нитевидных кристаллов Sі в области перехода металл-диэлектрик

На основі дослідження електропровідності ниткоподібних кристалів Si з діаметрами 40 ×10⁻⁶ м, легованих домішкою бору до концентрацій поблизу переходу метал-діелектрик (ρ300К = 0,94 ÷1,68 ×10⁻⁴ Ом•м) у температурному інтервалі 4,2 ÷70 К, частотному діапазоні 0,01 ÷250 ×10³ Гц виявлено, що імпеданс зразків в залежності від температури має ємнісний (4,2К – 20 К) та індуктивний (30 – 70 К) характер, величина якого залежить від концентрації легуючої домішки. На основі досліджень кристалів методом імпедансної спектроскопії обговорено відмінність поведінки імпендансу зразків з різною концентрацією легуючої домішки.Introduction. The paper deals with investigation of impedance spectroscopy of Si whiskers with doping concentration in the vicinity to metal-insulator transition in the region of low (4,2 – 70 K) temperature and frequency range 0,01 – 250 ×10 ³ Hz. Experimental results. The silicon whiskers were grown by chemical vapour deposition method in closed bromine system. The whiskers of 40 ×10 ¯⁶ m in diameter have boron concentration from 2×10 18 to 2×1019 сm ¯³. The impedance spectroscopy of Si whiskers was investigated with use of Lock-in amplifier in the region of low (4,2 – 70 K) temperature and frequency range 0,01 – 250 ×10 ³ Hz. The investigations showed that in the range of zone conductance (T= 30 – 70 K) the whisker impedance has inductive character, while at the range of impurity conductance (T = 4,2 – 20 K) impedance changes to capacity character. The reduction of impurity concentration at dielectric side of metal-insulator transition leads to decrease of the whisker capacity in the range of low temperatures. Discussion. An inductive character of whisker impedance is explained skin-effect of conductance in thin whisker, while capacity character of the whisker impedance is connected with hopping conductance on impurity band. Conclusions. Character of changes of Si whisker impedance conductance is discussed in the frame of hopping conductance on impurity band, which takes place at low temperatures.В результате выполненных исследований электропроводности нитевидных кристаллов Si с диаметрами 40 ×10⁻⁶м, легированных примесью бора до концентраций вблизи перехода металл-изолятор (ρ300К =0,94 ÷ 1,68 ×10⁻⁴ Ом м) в температурном интервале 4,2÷70 К, частотном диапазоне 0,01 – 250 ×10 ³ Гц обнаружено, что импеданс образцов в зависимости от температуры имеет емкостный (4,2 – 20 К) и индуктивный (30-70 К) характер, величина которого зависит от концентрации легирующей примеси. Исходя из результатов исследований кристаллов методом импеданс-ной спектроскопии обсуждены отличия поведения импенданса образцов с различной концентрацией легирующей примеси

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr\"odinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199