Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Computer simulation of some dynamical properties of the Lorentz gas

We carried out molecular dynamics simulations of a Lorentz gas, consisting of a lone hydrogen molecule moving in a sea of stationary argon atoms. A Lennard-Jones form was assumed for the H₂-Ar potential. The calculations were performed at a reduced temperatureK ^* =kT/_{H 2–Ar} = 4.64 and at reduced densities ^*= _{Ar Ar} ³ in the range 0.074–0.414. The placement of Ar atoms was assumed to be random rather than dictated by equilibrium considerations. We followed the trajectories of many H₂ molecules, each of which is assigned in turn a velocity given by the Maxwell-Boltzmann distribution at the temperature of the simulation. Solving the equations of motion classically, we obtained the translational part of the incoherent dynamic structure factor for the H₂ molecule,S _tr(q, ). This was convoluted with the rotational structure factorS _rot(q, ) calculated assuming unhindered rotation to obtain the total structure factorS(q, ). Our results agree well with experimental data on this function obtained by Egelstaffet al. At the highest density ( ^*=0.414) we studied the dependence ofS(q, ) on system size (number of Ar atoms), number of H₂ molecules for which trajectories are generated, and the length of time over which these trajectories are followed.     

Special frequencies and Lifshitz singularities in binary random harmonic chains

We consider a one-dimensional chain of coupled harmonic oscillators; the mass of each atom is a random variable taking only two values (M or 1). We investigate the integrated density of statesH(²) near special frequencies: a given frequency _s with rational wavelength becomes special if the mass ratioM exceeds a certain critical valueM _c . We show thatH has essential singularities of the typesH _sg exp(–C ₁ ¦²– _s ² ¦^–1/2) or exp(–C ₂¦²– _s ² ¦^–1), according to the value ofM and the sign of (²– _s ² ). The Lifshitz singularity at the band edge is analyzed in the same way. In each case, the constantC ₁ orC ₂ is evaluated explicitly and compared with a vast amount of numerical work. All these exponential singularities are modulated by periodic amplitudes. The properties of the eigenfunctions with frequencies close to the special values are also discussed, and are illustrated by numerical data.     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

Some exact models for nonspherical collapse.I

Evolution of incoherent matter distributions with cylindrical, pseudoplanar, and toroidal symmetries is considered. The system is described in terms of the scale factora (R, T) and the anisotropy factor (R, T) of the (x², x³ surfaces. A number of exact solutions is obtained under the assumptions=(a), =(R), and=(T) and their physical properties are breifly discussed. In particular, the solution with=(T) is noncollapsing and describes a matter distribution with unchanging density.     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains

We study the integrated density of statesH( ²) of a chain of harmonic oscillators with a binary random distribution of the masses. We show in particular that there is a dense set of values of the squared frequency for which the differenceH( ²+)-H( ²) has a singularity of the type ¦¦², multiplied by a periodic function of ln ¦¦, where the exponent and the period depend continuously on ². In the region where < 1/2,H is not differentiate on a dense set of points. The same type of singularities is also present in the Lyapunov coefficient.     

Localization in general one dimensional random systems,I. Jacobi matrices

We consider random discrete Schrödinger operators in a strip with a potentialV (n, ) (n a label in and a finite label across the strip) andV an ergodic process. We prove thatH ₀+V has only point spectrum with probability one under two assumptions: (1) Theconditional distribution of {V (n,)} _n=0,1;all conditioned on {V } _n0,1;all has an absolutely continuous component with positive probability. (2) For a.e.E, no Lyaponov exponent is zero.Research partially supported by USNSF grant MCS-81-20833     

Low frequency limits of third-order harmonic coefficients for atomic hydrogen in any level of discrete energy spectrum

In this paper the analytical expression is derived for the third-order optical harmonic coefficients x _abcd ^v (,,) of the atomic hydrogen at very low frequencies 0 in many level of the discrete energy spectrum.The author expresses his thank to Prof. Nguyen Van Hieu for suggesting the problem and fruitful discussions.     

Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation

We consider the Cauchy problem for the two-dimensional vorticity equation. We show that the solution behaves like a constant multiple of the Gauss kernel having the same total vorticity as time tends to infinity. No particular structure of initial data ₀=(x, 0) is assumed except the restriction that the Reynolds numberR=|₀|dx/v is small, wherev is the kinematic viscosity. Applying a time-dependent scale transformation, we show a stability of Burgers' vortex, which physically implies formation of a concentrated vortex.Partly supported by Grant-in-Aid for Scientific Research No. B60460042, the Japan Ministry of Education, Science and Culture     

Localization of a high-power microwaves absorption in the cylindrical plasma column at ωLH ≪ ω ≪ ωce

This paper describes experiments which make it possible to determine the place of the absorption of electromagnetic waves in a cold (T _e=5–10eV) not fully ionized plasma column at _ce/=1 and _ce/> 1.The authors wish to thank L.Bárdo for helping with the experiments.     

830 nm emission in sodium vapor

We demonstrate that the intriguing 830 nm coherent emission, which is observed when sodium vapor is pumped with a high-power pulsed laser tuned near the 3S4D two-photon transition, is due to an axially phase-matched six-wave mixing process. This conclusion is based upon the observation of emission near 584 nm, which is coupled to the 830 nm emission in the six-wave mixing process: ₁+₂=2_L–_4D4P –_4P3D . In addition, we have observed coherent emission near 1.16 m, which is due to an analogous process involving cascade through the 4S (as opposed to the 3D) state. We calculate the wavelengths of all photons involved in these processes using the standard formulas of parametric wave-mixing theory, and show that they can be predicted to within experimental uncertainties. Finally we report observations of significant blue shifts of the 830 nm and 1.16 m emissions in a mixed sodium-potassium vapor. These shifts can be readily understood by considering the effect of the potassium on the frequency-dependent refractive index of the vapor. Due to these results, other recent interpretations of the 830 nm emission as stimulated excimer emission on the Na₂ 1³ _g ⁺ 1³ _u ⁺ band must now be rejected.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

On the spectrum of Schrödinger operators with a random potential

We investigate the spectrum of Schrödinger operatorsH of the type:H =–+q _i ()f(x–x _i + _i ())(q _i () and _i () independent identically distributed random variables,i ^d ). We establish a strong connection between the spectrum ofH and the spectra of deterministic periodic Schrödinger operators. From this we derive a condition for the existence of forbidden zones in the spectrum ofH . For random one- and three-dimensional Kronig-Penney potentials the spectrum is given explicitly.     

Possible use of a gas-discharge plasma in an oscillating field to modulate electromagnetic radiation

The conditions for resonance and signal cutoff are determined from the dispersion relation for the complex refractive index for a plane electromagnetic wave propagating in a gas-discharge plasma when a magnetic field H = H₀ + H₁e^jt is imposed on the plasma. The refractive index and absorption are calculated for circularly polarized waves as functions of the alternating magnetic field with _p, _b, andv as parameters. Possible observation of modulation of the transmitted signal is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 94–99, April, 1971.     

Radiation damping of waves in a cold magnetized two-component plasma

It is shown in this paper that the damping decrements of electromagnetic waves with right circular polarization and the decrements of plasma oscillations near the cyclotron and hybrid frequencies in a strong magnetic field _eBpe are proportional to the square of the cyclotron frequencies _eB and _iB. In a weak magnetic field _eBpe the damping decrements of all modes are proportional to the square of the plasma oscillation frequencies _pe, _pi. Taking account of ions results in a nonzero damping decrement for electromagnetic waves with left circular polarization.Deceased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 8–11, October, 1982.In conclusion, I am grateful to L. S. Kuz'menkov and P. Polyakov for constant attention to the research and for useful remarks.     

Dark Energy and Global Rotation of the Universe

We discuss the problem of universe acceleration driven by global rotation. The redshift-magnitude relation is calculated and discussed in the context of SN Ia observation data. It is shown that the dynamics of considered problem is equivalent to the Friedmann model with additional non-interacting fluid with negative pressure. We demonstrate that the universe acceleration increase is due to the presence of global rotation effects, although the cosmological constant is still required to explain the SN Ia data. We discuss some observational constraints coming from SN Ia imposed on the behaviour of the homogeneous Newtonian universe in which matter rotates relative local gyroscopes. In the Newtonian theory _r,0 can be identified with ^,0 (only dust fluid is admissible) and rotation can exist with _r,0 =^,0 0. However, the best-fit flat model is the model without rotation, i.e., ^,0 =0. In the considered case we obtain the limit for ^,0>-0.033 on the confidence level 68.3. We are also beyond the model and postulate the existence of additional matter which scales like radiation matter and then analyse how that model fits the SN Ia data. In this case the limits on rotation coming from BBN and CMB anisotropies are also obtained. If we assume that the current estimates are _m,0 ~ 0.3, _r,0 ~ 10^-4, then the SN Ia data show that ^,0 -0.01 (or ₀ > 2.6 · 10^-19 rad/s). The statistical analysis gives us that the interval for any matter scaling like radiation is _r,0 ( - 0.01, 0.04).     

CW coherent VUV radiation generated by resonant sum-frequency mixing in metal vapors

Resonant third-order sum-frequency mixing of continuous-wave visible and ultraviolet laser light is investigated in the metal vapors of Sr, Ca, Mg, and Zn. The laser radiation (with the frequencies ₁, ₂, and ₃) is generated by single-mode dye- and argonion lasers. The third-order nonlinear susceptibility is enhanced by tuning the laser frequencies 2₁ or ₁+₂ to a two-photon resonance. The wavelength of the generated coherent VUV radiation (with the frequency _VUV=3₁, _VUV=2₁+₂ or _VUV=₁+₂+₃) is tunable in spectral regions between 133 and 217 nm. For most conversion processes an additional enhancement of the nonlinearity is provided by an autoionizing level or by a highly excited state close to E=_VUV. With laser powers of 0.2–3 W the power of the generated sum frequencies is in the range of 5×10⁵–6×10¹⁰ photons s^–1 (0.5 pW–60 nW).     

Calculation of the dispersion of the third-order optical nonlinearity in C60 films

Using wave functions determined from ground-state local-density calculations, we have calculated the wave-dispersed free response of the optical nonlinear polarizability ⁽³⁾(–3;,,), for the C₆₀ molecule and ⁽³⁾(–3;,,) i.e. Third-Harmonic Generation (THG) for films using a sum-over-states approach. The influence of screening was determined by applying an external static electric field in separate selfconsistent calculations to evaluate induced dipole moments which was used to determine the static linear and nonlinear polarizabilities. The polarizabilities calculated in the static limit were used to determine an effective screening parameter which was, in turn, used together with an RPA approach to calculate screened wave-dispersed, third-order nonlinear optical properties such as ⁽³⁾(–3;,,) and ⁽³⁾(–3;,,). Comparing evaluated polarizabilities with experimental values we found that the non-resonant free polarizability compares well in absolute magnitude with experimental results. Inclusion of screening results in a polarizability about two orders of magnitude below the experimental values.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Linear and non-linear ac response of the stochastic classical model for sliding charge density waves

A comprehensive study of the ac response properties of the classical stochastic model for sliding charge density waves (CDW) in quasi one-dimensional metals is made by numerically solving the associated Fokker-Planck equation. Above the conductivity threshold a noise mechanism is indispensable to give finite line widths to the resonances of the applied ac signal of frequency with the narrow band noise frequency _OSC inherent in the model. In the present investigation a current noise of strengthT _N proportional to the CDW current is used in the Fokker-Planck equation in order to model the broad band current noise frequently observed above threshold. The present model thus incorporates three characteristic frequency scales: _OSC,T _N ,and a crossover frequency _OSC. Results are evaluated for the ac conductivity (;E ₀,E ) as function of frequency , dc bias electric fieldE ₀ and ac signal field strengthE . ForE 0 the linear ac response is obtained by a separate treatment of the Fokker-Planck equation. The resonances near =_OSC are studied in detail. Strong ac signals reduce the response at the fundamental resonance and lead to a harmonic interference structure nearn=_OSC. The overall agreement of the present results with recent measurements of the linear ac response is not good. In reality our results seem to be superimposed on a background not reproduced by the classical model with one cross over frequency. However, the peak in Im (;E ₀,E =0) vs.E ₀, when the narrow band noise frequency is near , is well reproduced. The spectral width of this peak which corresponds to the inductive dip in the susceptibility is studied as function of current noise strengthT _N .The results stress the need for a complete Fokker-Planck treatment sinceT _N is not simply related to the line width.