Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of () at =0 above the AT line to a power law behaviour ()(–i) ^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to ^1/v , where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as ^1–1/v . The average relaxation time diverges as ^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i) ^v at and below the AT line.     

Influence of boundary conditions on square bond percolation nearpc

The influence of boundary conditions on square bond percolation for system sizes ranging from 10×10 to 240×240 is studied for the quantitiesP , , the effective percolation threshold and the finite-size scaling relations forP and . The Monte Carlo simulations suggest that free edges approximate the infinite system as well as the more complicated periodic boundary conditions.     

Nonlocality in (1/N)-expanded nonrenormalizable interactions

Nonrenormalizable interactions are studied on the example of the (1/N) ₆ ⁴ model with interaction via the collective = ² mode. In 4<d<6 dimensions, the model is nonrenormalizable by power counting but it does not require more subtractions than in the four-dimensional case. In six dimensions, nonrenormalizability is essential: There are two induced couplings ³ and . The ³ coupling strength can be determined from the requirement that the effective potential has a minimum at ² = = 0. The nonlocal formafactor produced by an infinite number of insertions cannot be determined uniquely, however the ambiguity concentrates in the leading order only. We construct this formfactor using the method of Efimov and Mogilevsky. The resulting theory satisfies unitarity, microcausality and correct spectral properties.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Mechanism Study for Thermal/Electric Field Poling of Fused Silica

On the basis of the experimental reports, the mechanism of the second-order susceptibility ⁽²⁾ for the thermal/electric field poling of fused silica is analyzed, and expressions for ⁽²⁾ are detailedly derived and numerically calculated for the first time. By comparison the theoretical value of ⁽²⁾ with the experiment results, we propose that the effective ⁽²⁾ is created via both the interaction of the intense electric field with the third-order susceptibility ⁽³⁾ and the dipole orientation. The theoretical results show that, in the differently applied voltage, the dipole orientation and ⁽³⁾ play different role in the formation of ⁽²⁾. This theory successfully explains some experiment results.     

A relationship between asymmetric Lévy-stable distributions and the dielectric susceptibility

This paper, as a complement to the work of Montroll and Bendler, is concerned with the Lévy-stable distributions and their connection to the dielectric response of dipolar materials in the frequency domain. The necessary and sufficient condition for this connection is found. The presented probabilistic analysis is based on the mathematically correct representation of the meaning of the relaxation function of a system of dipoles and shows why the same form of a distribution of relaxation rates, namely, the completely asymmetric Lévy-stable distribution, should apply in all different relaxing systems. This is in contrast to the traditional definition of the relaxation function, expressed as a weighted average of exponential relaxation functions, which does not explain the universality of the dielectric relaxation law. It also follows from the present considerations that not only is the imaginary part () of the dielectric susceptibility directly related to the Lévy-stable distribution (as was found by Montroll and Bendler), but so is the real part(). As a consequence the relation()/()=cot(n/2) for> _p and 0<n<1, implied by experimental results, is obtained.     

Theoretical Study for Wavelength Conversion of Cascaded Second-Order Nonlinearity in Silica Fiber

In this paper, A novel wavelength divison multiplexing (WDM) nets is proposed by use of cascaded second-order nonlinearities (⁽²⁾:⁽²⁾) in the D-fiber grating after periodically thermal/electric-field poling, and is theoretically analyzed for the first time. The coupled mode equations of the ⁽²⁾:⁽²⁾ nonlinearities are derived, and the analytic expressions for the electric-field amplitude of converted light wave and the conversion efficiency are obtained under the small signal approximation, which are well consistent with numerical calculations. Both analytic expressions and numerical results show that, under the phase matching, is proportional to the logarithm of the square of pump light power, and the 4th power of the grating length L and the second-order nonlinearity d. The calculated results also show that and of this fiber grating can be reached over -17dB and 120nm, respectively. With the increase of L, increases rapidly while decreases quickly. The results of simulated calculations and theoretical analysis show that the cascaded ⁽²⁾:⁽²⁾ process is different from quasi-phases-matched difference-frequency generation.     

An attempt at a phenomenological interpretation of the influence of a polarizing field on piezoelectric resonators

The change in frequency of quartz piezoelectric resonators in a d-c electric polarizing field cannot be explained merely by a change in the dimensions of the resonator due to the polarizing field caused by the inverse piezoelectric effect and electrostriction. We are forced to admit that the elastic constants also change in a polarizing field. A phenomenological interpretation of the influence of a d-c electric polarizing field on the frequency of quartz resonators is proposed here, based on newly introduced quantities characterizing such a change. In conclusion it is shown in what way the quantities, on which the phenomenological theory is based, can be determined experimentally.

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The author would like to thank Dr. J. Tichý for carefully reading the paper, for valuable discussion and numerous remarks on style and subject matter, which greatly helped to improve the text. He is also indebted to V. Janovec, C. Sc., for some new aspects and the exceptional interest with which he reviewed the paper.     

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     

A contribution to direct processes in the Co59(p,n) reaction forE p ∼ 6·5 MeV

Nuclear emulsions were used to study the energy spectrum and forward-backward asymmetry of neutrons from the Co⁵⁹(p,n) reaction forE _p 6·5 MeV. It was found that the decay of the compound nucleus makes a maximum contribution of 50% to the reaction yield. Energies of some excited states of the Ni⁵⁹ nucleus were also determined.

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Co⁵⁹(p,n) E _p 6,5 MeV

- Co⁵⁹(p,n) E _p 6,5 MeV. , 50%. , Ni⁵⁹.

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The authors would like to thank all those who helped in this work, particularly all members of the cyclotron group of the Nuclear Research Institute of the Czechoslovak Academy of Sciences, who so willingly helped with the irradiation, and H. Koutová from the Faculty of Technical and Nuclear Physics, who carefully measured the emulsions. Our thanks are also due to R. Krejová from the Faculty of Technical and Nuclear Physics for developing the emulsions and J. Kopecký from the Nuclear Research Institute for providing the cobalt target.     

The scattering of waves by a periodic surface

The paper derives a general formula for the scattering of electromagnetic (or sound) waves from a periodic, perfectly conducting (or perfectly rigid) surface. No restrictions are imposed on the angle of incidence, the size of the surface or the degree of roughness. Except for the basic Kirchhoff approximation, the method is exact. The results confirm, generalise or correct special cases obtained by more complicated methods.

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Paramagnetic shift of μ+ in MnO and its time dependence

Conclusion The paramagnetic shift K of ⁺ in MnO is measured from 140K to 420K. K is negative at 14OK, increases rapidly with increasing temperature, but does not show a linear relation to the susceptibility . At T = 170K and 230K, the value of K depends greatly on the fitting time-range of the spectrum. These features are explained by a site change of ⁺ caused by its diffusion and trapping in the crystal.     

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

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The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

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In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

Radiative E1 decay of the1P1 level of charmonium in the sum rules of quantum chromodynamics

An analysis of the radiative decay¹P₁ ¹S₀ + of charmonium is performed by using the sum rules of quantum chromodynamics (QCD). A sum rule that allows for luon power corrections is obtained, and the decay width _c + is computed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 80–84, November, 1991.Finally, the author express thanks to professor R. N. Faustov for valuable advice and useful discussion of the resulting work.     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Über die an „Schwachen“ Grenzflächen Entstehenden Kopfwellen

Zusammenfassung In der vorliegenden Arbeit werden die Kopfwellen untersucht, die beim Auffallen einer harmonischen Schall-Kugelwelle auf die Ebene Grenzfläche zwischen zwei flüssigen Medien entstehen. Vorausgesetzt wird, daß die Grenzfläche schwach ist, d. h. daß die Geschwindigkeit der Schallwellen im Medium mit der Erregungsquelle nur um weniges kleiner ist als die Geschwindigkeit der Schallwellen im Medium ohne die Quelle.

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Magnetic susceptibility of a one-dimensional Fermi system and dielectric function of a two-dimensional Coulomb gas

A relation between the magnetic susceptibility(k, ) of an interacting 1-D Fermi system and the dielectric function(q) of a 2-D Coulomb gas is established. By applying a cluster-expansion technique and by using known results for the pair-correlation function of the Coulomb gas we obtain a number of expressions for(q) which apply in different regions of theq-plane and in different temperature intervals. These results supplement the existing picture of the transition from non-metallic to metallic behaviour occurring in the 2-D Coulomb gas as the temperature increases. The relation between(q) and(k, ) is then used to derive explicit expressions for(k, ) from these results for(q). The change in the dielectric response of the 2-D Coulomb gas is reflected by a change in the magnetic response of the 1-D Fermi system: as a function of the spin non-flip coupling constant the susceptibility of the Fermi system changes from normal paramagnetic behaviour to non-magnetic behaviour characteristic of a bound singlet-spin ground state, as decreases. Our result for the gap in the spin excitation spectrum of the Fermi system is in agreement with the results of other authors.On sabbatical leave from Institut für Theoretische Physik, TU Hannover, GermanyWork at U.C.S.B. supported in part by the National Science Foundation     

Determination of accuracy in measuring the parameters of tetragonal and hexagonal lattices

The procedure for determining the accuracy when measuring the parameters of tetragonal and hexagonal lattices is described. The accuracy can easily be calculated for all common methods by means of graphically represented functions. The relations derived can be used as quantitative criteria for the suitability of the combination of lines from which the lattice parameters are to be determined.

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The nonrelativistic Schrödinger equation in “quasi-classical” theory

The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field (x, t), interacting with each other via nonlinearity in the equation of motion for . The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from a configuration-space wave function (x ₁,x ₂,t), and that the theory requires that satisfy the two-particle Schrödinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schrödinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials.     

Die Sättigungseffekte Bei Senkrechtfeldresonanz in YIG

Zusammenfassung Messungen des Imaginärteils der Suszeptibilität als Funktion der Mikrowellenfeldstärkeh wurden bei Hauptresonanz an Proben aus reinem und mit Dysprosium dotierten Yttrium-Eisen-Granat durchgeführt. Die Gestalt der (1/h)-Kurven urde auf Grund einer früher veröffentlichten Theorie behandelt. Der an der Probe 3 gemessene Verlauf von kann befriedigend mit Hilfe des Modells der unabhängigen Spinwellen interpretiert werden. Dasselbe gilt für die Messung an der Probe 2 mit Gleichfeld in [111]-Richtung. Die Steilheit der quasilinearen Kurvenabschnitte ist bei diesen(1/h)-Kurven von der GrößeH/H _k abhängig. Die Spinwellenhalbwertsbreite wurde auf Grund des benützten Modells mit Hilfe des Maximums der Größeh bestimmt. Der an der Probe aus reinem YIG gemessene Verlauf von stimmt für den Fall des Gleichfeldes in [100]-Richtung mit dem Modell der stark gekoppelten Spinwellen gut überein. Die Messung an dieser Probe mit Gleichfeld in [111]-Richtung weist einen anderen Verlauf der (1/h) Kurve auf, welcher nicht durch den Einfluß der magnetokristallischen Anisotropie der YIG erklärt werden kann. Dies sollte eher der Anisotropie der GrößeH _k zugeschrieben werden und wir vermuten, daß die letztgenannte Messung ein Verhalten widerspiegelt, das irgendwo zwischen den mit der Theorie diskutierten Extremfällen liegt. Dasselbe kann von der Messung an der Probe 2 mit Gleichfeld in [100]-Richtung gesagt werden.

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Saturation effects at main resonance in YIG

The imaginary part of the susceptibility at main resonance was measured as a function of the microwave field intensityh on samples of pure YIG and also on YIG doped with Dy. The experimental results are compared with a theory published earlier. In particular the form of the(1/h) curves is discussed and also the way in which the spin wave relaxation frequencies can be determined.