Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Laser-selective enrichment of 3d-states of the Ca II ion for detecting rare radioactive isotope calcium-41

For the detection of the rare radioactive isotope⁴¹Ca, the possibilities of the earlier-proposed initial-state enrichment by continuous-wave laser radiation are examined. It is shown that the enrichment 10¹⁴ of 3d-states of the ion Ca II can be reached. As the method of enriched-state detection, the process of resonant charge exchange is analysed. For a further increase of the selectivity, the repetition of the cycle initial state enrichment plus resonant charge exchange is discussed.     

On singularities in the disordered phase of a driven diffusive system

Using renormalization group techniques, we investigate the large distance behavior of a driven, interacting lattice gas in the disordered phase. Unlike the equilibrium Ising model, its behavior, ford>2, is controlled by aline of fixed points, each of which is interpreted as a dynamical system violating the fluctuation-dissipation theorem (FDT). As a consequence, correlation functions at large distances typically decay according to a power law instead of an exponential. Ford2, the renormalization group flows towards an FDT-satisfying fixed point, which corresponds to the high-temperature, strong-drive limit. In the steady state of such a model (a driven, free lattice gas), correlations are known to be exactly zero. Nevertheless, our correlations are still dominated by power laws, since the FDT-breaking operators aredangerously irrelevant (marginal ind=2). Thus, for anyd, the long wavelength properties cannot be obtained by taking either the non-interacting or theT limit, unlike for the equilibrium Ising model.     

The effect of the orientation of zinc single crystals and of the rate of growth on the direction of cell substructure

The effect of the orientation of zinc single crystals and the rate of growth on the direction of the formation of cellular substructure is observed. A model accounting for the observed dependences is proposed.

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Interface formation and a structural phase transition for the spherical model of ferromagnetism

A detailed analysis is reported examining the local magnetic susceptibility (r), in relation to the correlation functionG(R) and correlation length , of a spherical model ferromagnet confined to geometry =L ^{d –d} × ^d ( ^d 2,d>2) under a continuous set oftwisted boundary conditions. The twist parameter in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For _j 0, jd-d, no seams are present except at infinity, whereas if _j = 1/2, impurity saturation occurs. For 0 < _j < 1/2 the physical domain _phys =D ^{d –d} × ^d (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T ₀). Below that temperature (T>T ₀), seams are frozen at the same position (DL/2,d-d'=1), revealing a smoothly varying largescale structural phase transition.     

Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum

We consider a system ofN hard spheres in the Boltzmann-Grad limit (i.e.d0,N,Nd ^2–1>0, whered is the diameter of the spheres). If is sufficiently large, and if the joint distribution densities factorize at time zero, with the one particle distribution decaying sufficiently rapidly in space and velocities, we prove that the time evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum. This result improves and is based on a previous paper [1], valid only in two dimensions.Partially supported by MPI and GNFM (CNR)     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

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.     

Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].     

Bound on the mass gap for finite volume stochastic ising models at low temperature

We consider a sequence of finite volume Z ^d ,d2, reversible stochastic Ising models in the low temperature regime and having invariant measures satisfying free boundary conditions. We show that associated with the models are random hitting times whose expectations, regarded as a function of , grow exponentially in ||( ^d-1)/d ; moreover, the mass gaps for the models shrink exponentially fast in ||( ^d-1)/d . A geometrical lemma is employed in the analysis which states that if a Peierls' contour is sufficiently small relative to the faces of , then the fraction of the contour tangent to the faces is less than a constant smaller than one.     

A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

Comparison of (π− d→nn withdσ(π+ d→pp) to test charge symmetry in the Δ-region

First results on ^– d are reported. The measurements were made using 8 specially designed neutron counters, which were carefully calibratedin situ. The differential cross sections atT =142, 180, 217, and 254 MeV were obtained at four angles between 0° and 90°, they are compared to ⁺ d pp data measured at the same energies and angles with the same setup. At every beam energy, the shape of the angular distributions of ^– d nn and ⁺ d pp is the same to ±2%. The absolute cross sections differ by 1 to 10%. The error in this comparison is ±4% implying a small violation of charge symmetry.Dedicated to Prof. I. laus on the occasion of his 60th birthdayDeceased     

Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Convergence of Nelson fiffusions

Let _t, _t ⁿ ,n1, be solutions of Schrödinger equations with potentials form-bounded by –1/2 and initial data inH ¹( ^d ). LetP, P ⁿ ,n1, be the probability measures on the path space =C(₊, ^d ) given by the corresponding Nelson diffusions. We show that if { _t ⁿ } _n1 converges to _t inH ¹( ^d ), uniformly int over compact intervals, then converges to in total variation t0. Moreover, if the potentials are in the Kato classK _d , we show that the above result follows fromH ¹-convergence of initial data, andK _d -convergence of potentials.     

Radius,perimeter, and density profile for percolation clusters and lattice animals

Monte Carlo simulation and series expansion shows the radius of gyration of large clusters withs sites each to vary ass with0.56 in two and0.47 in three dimensions at the percolation threshold, and with(d=2)0.65 and(d=3)0.53 for random lattice animals (zero concentration). Clusters up tos=100 were used. The perimeter of random animals approaches 2.8s for larges on the simple cubic lattice. Monte Carlo simulation of the Eden process (growing animals) up tos=5,000 indicates a systematic variation of about ±0.05 for the effective exponent=(s) and thus suggests that the true asymptotic exponents may be compatible with the predictions of hyper-scaling.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

The friction coefficient exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios , where and are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out onfinite systems. The three independent methods lead to estimates of which agree within statisticalerrors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold withstick boundary conditions, in the range 1/4.5 explored in the present simulations, with a hydrodynamic diameterd=. The analysis of the moleuclar dynamics data on the basis of Stokes' law withslip boundary conditions is less conclusive, although the right trend is found as / increases.     

Schrödinger Operators with Empty Singularly Continuous Spectra

Let H be a semibounded perturbation of the Laplacian H ₀ in L ²( ^d ). For an admissible function sufficient conditions are given for the completeness of the scattering system (H), (H ₀). If is the exponential function and if e^{– H} is an integral operator we denote the kernel of the difference D = e^{– H} – e^{– H} ₀ by D (x, y), > 0. The singularly continuous spectrum of H is empty if^d dx ^d dy |D(x,y)| (1 + |y|²)< for some > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions.     

Fluctuation corrections of the turbulence spectrum by renormalization group methods

We apply the renormalization group idea to a stationary probability distribution which is supposed to represent a turbulent fluid. In contrast to the common procedure the R.G.T. is defined by eliminating successivelylow wave numbers instead of integrating from largek. This means that instead of starting from the short distance fluctuations, as near phase transitions, the procedure corresponds to the von Weizsäcker-Heisenberg averaging over nestedr-space volumes of decreasing size.Ifd>2 we find a non-trivial fixed point of the R.G. equations. It is stable and attractive for every reasonable choice of the distribution function parameters. The only existing critical exponent is the field dimension. Its anomalous part gives rise to a correction >0 in the exponent of the turbulence spectral function,E(k)k ^–(5/3+). The macroscopic part of the correlation function's scaling exponent, Kolmogoroff's 5/3, is determined by the scaling behaviour of the noise parameter which governs the probability distribution. The correction is explained as being due to the fluctuations. is calculated by-expansion of the R.G.T.,=d–2. One gets ²; extrapolating to=1 it is1/8.Herrn Prof. Dr. G. Ludwig zum 60. Geburtstag gewidmetThis work has been done in part at the Max-Planck-Institut für Physik und Astrophysik, München. I would like to thank Prof. W. Zimmermann and Prof. W. Götze for their warm hospitality     

Wedge-screw dispiration in smectic liquid crystals with antiferroelectric order

Using the approximative expression for the elastic energy density of the antiferroelectric (AF) liquid crystal the elastic self-energy of (, b)-wedge-screw dispiration is estimated. Then the elastic interaction between (, b)-wedge-screw dispiration and (2)-wedge dischnation in AF liquid crystals is investigated. The attraction of dislocation part of dispiration with (2)-wedge disclination can lead to the formation of (3)-wedge-screw dispiration. When (2)-wedge disclination is trapped by (2d)-screw dislocation the resulting (2, 2d)-dispiration can dissociate into a pair of two (, d)-dispirations.The authors express their thanks to Professors A. Fukuda, H. Takezoe, Dr. Y. Takanishi and to Dr. K. Miyachi for discussions concerning their experimental observations of (3, d)-wedge-screw dispirations and (, d)-twist-edge dispirations in AF structures. This work was supported by the grant No. 19062 from Acad. Sci. Cz. R. and also benefited by the grant No.: 202/93/155 from the Grant Agency of the Czech Republic.