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     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

Theory of electric field-induced optical second harmonic generation in semiconductors

The nonlinear optical coefficientd _ij(kl) (2, 0,, ) for electric field-induced optical second harmonic generation in semiconductors is calculated by means of a perturbation treatment. The result is given directly as a Brillouin zone integral over a resonant energy denominator. A simplified energy band structure model is used to carry out the Brillouin zone integral. The analytic closed-form expression ford _ij(kl) (2, 0,, ) thus obtained permits the calculation of the absolute value of its spectrum from available energy band parameters. The dispersion ofd ₁₁₍₁₁₎ (2, 0,, ) of Ge is numerically calculated, second harmonic photon energies being close to theE ₀ andE ₁ gaps. The results show pronounced resonant behaviours.     

The plasmon density of states of a layered electron gas

The plasmon density of states (DOS)p() of a layered electron gas (LEG) is studied theoretically. It is shown thatp() is a linear function of frequency as goes to 0, and then increases more rapidly as tends to the screened, three dimensional plasma frequency _p. We also study the partial densities of state for constantK andq _z , whereK andq _z are the magnitude of the transverse and perpendicular momentum transfers. A possible experimental probe for the plasmon DOS is discussed.     

Some exact models for nonspherical collapse. III

The gravitational nonradiative collapse of dust configurations in the presence of electromagnetic field is analyzed in terms of exact dynamical solutions for a wide range of spacetime symmetries: cylindrical, pseudoplanar, toroidal, and also spherical, planar, and pseudospherical [when the anisotropy factor of the (x ²,x ³) surfaces,(R, T), is replaced by a massless scalar field]. The condition that the collapse is nonradiative leaves three possibilities for the coordinate dependence of(R,T) (i)=(a),a (R, T) being the scale factor of the (x ²,x ³) surfaces, (ii)=(T), and (iii)=(R). Almost all (in the meaning indicated in the text) solutions for charged dust with=(a) and for dust in the external electromagnetic field with=(T) and=(R) have been obtained and discussed. A wideranging discussion concerning the topics of papers I–III is given. Special attention is paid to the question of horizon existence and formation and also the perspective of extension of the techniques developed onto the more realistic case of axial symmetry.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

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     

Subharmonic electromagnetic radiation from cavitons

In a high-power microwave-plasma system, it has been experimentally found that electromagnetic (em) radiation at subharmonic frequencies [specifically, (3/2)₀ and (5/2)₀] of the electron plasma frequency of the unperturbed state, ₀, can be emanated from cavitons which are resonantly driven by an intense em pulse (frequency ₀) in an unmagnetized inhomogeneous plasma. Electron oscillations at ~ (1/2)₀ are preferentially excited inside a deep (|n/n_c|0.5) caviton although this is not deep enough to resonantly support (1/2)₀ oscillations. The experimental results show that the coupling between the (1/2)₀ electron oscillations inside the caviton and the electron plasma waves at (3/2)₀, which is originally excited due to the mode conversion of the incident microwave at the resonant layer and which generates the caviton, produces a localized nonlinear current which emits em waves at (3/2)₀. A similar coupling between (3/2)₀ and ₀ frequencies can emit em waves at (5/2)₀. The model to explain the above new phenomenon is discussed.Institute of Research and Development, and School of High Technology for Human Welfare, Tokai University, Japan. Department of Physics, University of California, Los Angeles, California. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 5, pp. 596–616, May, 1994.     

Plasma instability in a strong,circularly polarized electromagnetic wave

Conclusions In summary, we have studied the parametric instability of a cold electron plasma in a strong, circularly polarized electromagnetic wave, taking into account the relativistic nature of the electron motion. We have shown that an instability of longitudinal waves occurs at frequencies _p/ and _p/, while an instability of transverse waves occurs at frequencies ₀±₀ and ₀±_p/. The results of a numerical solution of the dispersion relation for large pump amplitudes, in which case the approximation of a weak coupling between waves is not applicable, show that the growth rates and the bands of the instabilities increase with increasing pump amplitude. We have found that in the case of the excitation of electromagnetic plasma waves, even at low pump amplitudes, the relativistic nature of the electron motion can be of decisive importance for the effect.T. G. Shevchenko Kiev State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 19, No. 10, pp. 1481–1488, October, 1976.     

A Boltzmann map for quantum oscillators

We define a map on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points ofx. The map is the composition of a doubly stochastic map T^* and the quasifree reductionQ. Under mixing conditions onT, iterates of take any initial state to the Gibbs state, provided that the oscillator frequencies are mutually rational. We give an example of a system with three degrees of freedom with energies ₁, ₂, and ₃ mutually irrational, but obeying a relation n₁₁+n₂₂=n₃₃,n _i . The iterated Boltzmann map converges from an initial statep to independent Gibbs states of the three oscillators at betas (inverse temperatures) ₁,₂, ₃ obeying the equation n₁₁₁+n₂₂₂=n₃₃₃. The equilibrium state can be rewritten as a grand canonical state. We show that for two, three, or four fermions we can get the usual rate equations as a special case.     

Mathematical properties of gap-functions in strongly coupled superconductors

We consider the Dyson equation associated with the BCS superconducting state from a mathematical point of view. The Dyson equation gives rise to a modified gap equation that is similar to the BCS gap equation, but with a different kernel. We first show that for strong coupling (such that the McMillan parameter ||1) both the real and imaginary parts of the solution (E) of the modified gap equation alternate in sign as function of the excitation energyE, the periods being 4₀ for positive and 4₀/3 for negative . (₀ is the frequency of an Einstein spectrum of phonons). A closed, algebraic approximation to (E) is 2||₀log[cotan(E/ )]. Finally, the poles of the kernel of the integral equation are located in the complex-E plane. For the new-type, oscillatory solution of the modified gap equation the analogue of the causal (zero-temperature) Green's function is shown to have different analytic properties from those of the smooth Eliashberg solution of BCS theory.     

Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

Excited-state absorption and third-order optical nonlinearities in symmetric π-electron organic molecules

Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA _g B _u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.     

Generation of more than 40 laser emission lines from the ultraviolet to the visible regions by two-color stimulated raman effect

An intense and monochromatic laser beam consisting of more than 40 vibrational and rotational lines is generated by the stimulated Raman effect, when two-color laser beams separated by 590 cm^–1 are tightly focused into pressurized hydrogen. This phenomenon is reasonably explained by four-wave mixing; one beam is used for two-step excitation (₁+₁) to an imaginary level and another beam (₂) acts as a seed beam, generating a fourth beam (2₁–₂). Through cascade processes, so many laser emissions appear with a frequency difference of (₁–₂) in entire ultraviolet and visible regions.     

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.     

Classical “freezing” of plane rotations: A proof of the Boltzmann-Jeans conjecture

Using simple known methods and results of classical perturbation theory, especially those due to Nekhoroshev and Neishtadt, we study the energy exchanges between the rotational and the translational degrees of freedom in a particular model representing the planar motion of a rigid body in a bounded analytic potential. We prove that, if the angular velocity is initially large, then the energy exchanges are small,O( ^–1), for times growing exponentially with, |t|exp. We also deduce that in a scattering process from a (smooth) potential barrier, the overall change in the rotational energy of the incoming body is exponentially small in, exp(–. The results are interpreted in the light of an old conjecture by Boltzmann and Jeans on the existence of very large time scales for equilibrium in statistical systems containing high-frequency degrees of freedom (purely classical freezing of the high-frequency degrees of freedom); the rotating object is, in this interpretation, a (classical) molecule, which moves in an external field, or collides with the wall of a container. Two different limits of large are considered, namely the limit of large rotational energy, and (as is interesting for the molecular interpretation) the limit of point mass, at finite rotational energy.     

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).     

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.     

Normal mode configuration in an inorganic medium containing defects

The vibrational structure in an inorganic medium containing defects is analyzed as a function of the frequency of the applied field. Since the dispersion relations for the medium are nonlinear, the configuration of the normal modes depends differently upon and . It is shown that exponential damping of the optic branches is observed for <₀, and that the structure of these modes changes significantly over the range 0<<₀, so that only in the neighborhood of ₀ does it correspond to long wavelength vibrations with configurations of stress deviator waves.Institute for the Physics of Strength and Materials Science, Russian Academy of Sciences, Siberian Division. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 87–90, October, 1994.