Continuously Varying Exponents in a Sandpile Model with Dissipation Near Surface

We consider the directed Abelian sandpile model in the presence of sink sites whose density f_t at depth t below the top surface varies as ct^–. For >1 the disorder is irrelevant. For <1, it is relevant and the model is no longer critical for any nonzero c. For =1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this dependence exactly, and verify the results with simulations.     

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.     

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.     

Initial magnetic susceptibilities of iron and nickel aerosol powders

The dependence on angle is considered for the hysteresis-free initial susceptibilities _a and _ar together with the initial susceptibility _o for iron and nickel aerosol powders, as well as the effects on these characteristics from changes in powder packing density. Estimates are made of the negative-interaction fields, and a quantitative comparison is made between the observed _ar() and theoretical values by means of the pair model. The correlation between the experimental and theoretical relationships confirms the concepts used on the predominant effects from magnetostatic interaction in the mechanism for magnetization reversal in powders of materials with low anisotropy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, pp. 40–43, July, 1984.     

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.     

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.     

Seventh and ninth order nonlinear susceptibility measurement in alkali metal vapour

We report the first experimental measurement and theoretical estimation of seventh _eff ⁽⁷⁾ and ninth _eff ⁽⁹⁾ order effective nonlinear susceptibilities. The correlation of ninth, seventh and fifth harmonic signal efficiencies in various phase-matched mixtures of Ar (or Xe) and sodium atoms, is experimentally investigated. Using direct and cascade processes of harmonic generation, the modulus ratio is measured for the higher nonlinearities, which allows an estimation of _eff ⁽⁷⁾ and _eff ⁽⁹⁾ from the lower order optical susceptibilities. Results from numerical calculations of atomic nonlinear susceptibilities up to the ninth order, accounting for the discrete spectrum and the continuum, are presented.     

Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”

Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization |M|, susceptibility) and percolation cluster properties relating to the physical clusters, namely the Fortuin-Kasteleyn clusters (percolation probability P , percolation susceptibility _p, cluster size distributionn _l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, P being identical to |M| in the thermodynamic limit, while finite-size corrections differ. In contrast, _p differs from even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to, but not to _p. NearT _c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.     

N=2 topological gauge theory,the Euler characteristic of moduli spaces,and the Casson invariant

We discuss gauge theory with a topologicalN=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space and the partition function equals the Euler number () of . We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of connections. As a consequence of these considerations we propose the Euler number () of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. We also comment on the possibility of constructing a topological version of the Penner matrix model.From Oct. 1992: ictp, P.O. Box 586, I-34100 Trieste, Italy     

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.

     

Scaling of the surface tension of phase-separated polymer solutions

The tension of the interface between the equilibrium phases of a phase-separated polymer solution is obtained in the simplest mean-field approximation from the functional equation for the composition profile of the interface. For temperaturesT near the critical solution temperatureT _c, i.e., for Flory parameter near _c, and for high degrees of polymerizationN, the profile and tension scale with=N ^1/2(– _c), just as do the compositions of the coexisting phases in mean-field approximation. The surface tension in the asymptotic limitN, _c at fixedx, is found to be given bya ²/kT _c (2c'/c)^1/2 N ^-5/4(x), wherea is the lattice spacing of an underlying lattice (or, roughly, the length of a monomer),c andc are the vertical and total coordination numbers of the lattice, and(x) is a scaling function, known for allx, with the asymptotic behavior asx0 and asx. The latter implies that becomes independent ofN asN at fixedT nearT _c; the former implies that becomes proportional toN ^–1/2(1–T/T _c)^3/2 asTT _c at fixedN1, as found previously.     

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.     

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 Magnetische SuszeptibilitÄt von Kristallinem n-CdGeAs2

The specific magnetic susceptibility of polycrystalline and powdered samples was measured between 77 °K and 570 °K. This dependence was interpreted in intrinsic range suggesting the susceptibility is given as a sum of contributions of the lattice ^G and of free carriers _L. The temperature dependence of the lattice susceptibility _G= _G ⁰ +T was checked: _G ⁰ =–2·35× ×10^–7, =4·5×10^–11. The contribution _L enabled to check the effective mass of holes m_h=0·25m₀ suggesting m_em_h.

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Herrn A. Hrubý gilt mein Dank für die Vorbereitung des polykristallinen Ingots von CdGeAs₂.     

Dynamics of vector spin glasses: The Gabay-Toulouse line

The dynamics of ann-component vector spin glass with infinite range interactions are investigated near and above the Gabay-Toulouse (GT) line. The local transverse susceptibility _T for 0 varies along the whole GT lineT _c1 (H) as ^v , with a field and temperature independent critical exponentv=1/2. The longitudinal susceptibility _L () remains analytic for all (T, H)T _c1 (H), except for a cross-over fromv=1 tov=1/2 forH0 at the freezing temperatureT=T _f . The dynamic susceptibilities _T () and _L () are already coupled above the GT line via self-energy terms. BelowT _c1 (H), this coupling is strongly enhanced by other mechanisms.     

On the magnetic susceptibility of Pd1−x Ag x in the range 0.5≦x≦1

The weak variation of the magnetic bulk susceptibility of Pd_1–x Ag _x with temperature T and silver mole fractionx within 0.5x1 has been investigated in the range 5KT400K. Experimental evidence can be given for an intersection point of the susceptibility isotherms (T=const,x) atx=0.55. The observed dependence of on T andx is interpreted by means of a semiphenomenological alloy susceptibility function (T,x).     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Magnetic moments and the high field susceptibilities of MnFe2O4

An extended version of the noncollinear spin model bySawatzky et al. is developed to derive a dependence of the differential high field susceptibility on the degree of inversion of the ferrite MnFe₂O₄. Using the available data on the main molecular field coefficients it is shown that the present model imposes restrictions on values of. Determination of from the measurements of the field dependence of the saturated moments at low temperatures on samples with varying degrees of inversion reveals good quantitative agreement with the present model.     

Aspects of χ and ψ production in polarized proton-proton collisions

Several topics of relevance to low transverse momentum and _1,2(c ) production in polarized proton-proton collisions are discussed. The leadingO( _S ³ ) contributions to the lowp _{T 1} production cross-sections viagg, qg, andq initial states are calculated as well as the corresponding spin-spin asymmetries. We find that ₁ production increases relative to direct and ₂ production, providing up to 25% of the observablee ^* e ^– pairs arising from decays inpp collisions at s=500 GeV. The spin-dependence of ₁ production, however, is much smaller than for either direct or ₂ production and so will likely be far less useful than either process in probing the polarized gluon structure function of the proton. A subset of theO( _S ³ ) radiative corrections to ₂ production involving initial state quarks are also performed and compared to leading ordergg₂ predictions.     

Buoyancy forces in magnetic fluids

The ponderomotive force on a macroscopic body in a magnetic fluid is calculated by a hydrodynamic approach. The resulting equations are generally valid, neither small susceptibilities nor stationarity are assumed. The simple and widely-used formulaV(M-M ^bg )H is recoverd in linear order of ; magnetostrictive effects are shown to contribute in the order ³. The expressions derived here are definite and unambiguous, they do not depend on whether one starts from a theory in terms ofH, or in terms ofB: the correct evaluation of the contribution dV[-p] resolves the apparent contradiction between the force density expressions ₀ MH, orMB.