Phases of the number-theoretic spin chain

We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition functionZ()=(–1)/() at the inverse temperature _cr=2.     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

Kac-Moody symmetry of generalized non-linear Schrödinger equations

The classical non-linear Schrödinger equation associated with a symmetric Lie algebra =km is known to possess a class of conserved quantities which from a realization of the algebrak []. The construction is now extended to provide a realization of the Kac-Moody algebrak[, ^–1] (with central extension). One can then define auxiliary quantities to obtain the full algebra [, ^–1]. This leads to the formal linearization of the system.     

Inertial effects on the escape rate of a particle driven by colored noise: An instanton approach

A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation , where is a Gaussian colored noise with mean zero and correlator (t)(t')=(D/)exp(–|t–t'|/). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D0) limit. This yields an escape rateexp(–S/D), where the actionS is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an instanton of the theory. The extremal actionS is calculated analytically for smallm and for general potentials, and numerical results forS are displayed for various ranges ofm and for the typical case of the quartic potentialV(x)=–x ₂/2+x ₄/4.     

How often do simple dynamical processes have infinitely many coexisting sinks?

This work concerns the nature of chaotic dynamical processes. Sheldon Newhouse wrote on dynamical processes (depending on a parameter )x _x+1=T(x _n ; ), wherex is in the plane, such as might arise when studying Poincaré return maps for autonomous differential equations in IR³. He proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane, and that such parameter values would be dense in some interval. The fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes. We prove, for an apparently typical situation, that Newhouse's construction yields only a set of parameter values of measure zero.This research was supported in part by grants from the Air Force Office of Scientific Research AFOSR 81-0217, the Consiglio Nazionale delle Ricerche-Comitato per le Matematiche, and the National Science Foundation DMS 84-19110On leave from: Dipartimento di Matematica G. Castel nuovo Universita di Roma La Sapienza P. le Aldo Moro 5, I-00185 Rome, Italy     

Stimulated IR- and vacuum-UV emission following two-photon-excitation of molecular hydrogen using an ArF laser

Hydrogen molecules are excited by two 193 nm-photons [X¹ _g ⁺ E,F¹ _g ⁺ ;Q₀₂(1)] generated with a commerical oscillator-amplifier ArF laser. Stimulated emission is subsequently observed in the IR (=752.4 nm to 836.6 nm;E, FB) and in the VUV (=134.0 nm to 160.9 nm;BX) with a VUV conversion efficiency of 0.2%. The rotational fine-structure, the saturation behaviour, pump depletion as well as SRS-onset on and off two-photon resonance are investigated.     

Positron annihilation anomaly in the high-temperature superconductor YBa2Cu3O7−x

We have measured the ac susceptibility of a wire with a Nb core (1.27 mm diam.) and a Cu cladding (0.37 mm thickness) atT50 K andB0.1 mG. Due to its proximity to Nb, the Cu becomes fully superconducting. From the data we find a breakdown fieldH _b =1.2 (mG) and a coherence length =2.2T ^–1/2 (m) for the Cu, as well as a field penetration depth -34T ^1/2 (m) at the Cu/Nb interface.     

A discrete spectrum of solutions of the wave equation with strong cubic nonlinearity

The nonlinear wave equation, _tt –+³=0, has many solutions that are periodic in time and localized in space, all with infinte energies. The search for spherically symmetric solutions that are well represented by the simple approximation, (r, t)A(r) sin t, leads to a discrete spectrum of solutions{ _N (r, t; )}. The solutions are nonlinear wavepackets, and they can be regarded as particles. The asymptotic theory () of the motion of the guiding center of theNth wavepacket, in the presence of a specified potential, is characterized by an infinite mechanical mass and an infinte interaction mass, and they are compatible. The rest mass in the classical relativistic mechanics of guiding centers ism ₀ c ²= _N ; i.e. the spectrum { _N } determines a spectrum of Planck's constants.On leave (1972–73) Université de Paris VI, Département de Mécanique, 75 Paris 5^e, France.     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

The elastic coupling between longitudinal and transversal vibrations of isotropic rods I. Rods of square and rectangular cross-section

A new approximate method for theoretically calculating longitudinal vibration frequencies of isotropic homogeneous rods of square and rectangular cross-section is given. We divide a three-dimensional longitudinal vibration into three one-dimensional ones; the coupling between the principal strains in question is assumed to be linear, similarly as in the static case of simple tension. The coupling between the deformations is realized by variable coupling parameters or depending on the order of vibrations (contrary to Rayleigh's correction where Poisson's ratio is the coupling parameter). These parameters are defined by the condition that the corresponding frequency must be minimized (stationary).Up till now Giebe and Blechschmidt [2] have given the best approximate method of calculation. The series of their calculated frequencies corresponds to the measuredones nearly as well as the frequencies calculated by us. The theory described here, however, contains a richer spectrum of frequencies and at the same time explains the frequencies measured in the range of the so-called dead zone, which is the weak point of Giebe's and Blechschmidt's theory.

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. ; , . , ( , ). , ( ). [2]. , , . , , , , . . , .

     

ТЕМПЕРАТУРНАЯ ЗАВИС ИМОСТЬ ТЕРМОЭЛЕКТРОДВИЖУЩ ЕЙ СИЛЫ СЕРОГО ОЛОВА С ПРИМЕСЯМИ КАДМИЯ

- , - —183 —10 °.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

Beitrag zum problem der Exo-Emission von festkörpern

Zusammenfassung Es sind die Versuchsergebnisse des Studiums der Photoerscheinungen bei verschieden bearbeiteten Metallen (Au, Al, Pt) angeführt. Die Metallfolien wurden an der Luft mit UV-Licht bestrahlt und gleichmä\ig erwärmt. Die Ergebnisse wurden vom Gesichtspunkt der neueren Kenntnisse über Adsorption, Katalyse und Oxydation diskutiert. Daraus sind Folgerungen gezogen worden, die in manchen Fällen zu Bedenken über die Klärung der Exo-Emissions-Glow-Kurven zu führen scheinen.

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Au, Al, Pt . , . , . , .

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Ich möchte auch an dieser Stelle meinen besten Dank Frau K. Listoová aussprechen für die mit gro\er Sorgfältigkeit durchgeführten Versuchsreihen und K. Huml für die Hilfe bei der Bearbeitung der Versuchsergebnisse.     

On the Long Time Behavior of Infinitely Extended Systems of Particles Interacting via Kac Potentials

We analyze the long time behavior of an infinitely extended system of particles in one dimension, evolving according to the Newton laws and interacting via a non-negative superstable Kac potential (x)=(x), (0, 1]. We first prove that the velocity of a particle grows at most linearly in time, with rate of order . We next study the motion of a fast particle interacting with a background of slow particles, and we prove that its velocity remains almost unchanged for a very long time (at least proportional to ^–1 times the velocity itself). Finally we shortly discuss the so called Vlasov limit, when time and space are scaled by a factor .     

Duality for a Lorentz quantum group

We give the algebra _q ^/* dual to the matrix Lorentz quantum group _q of Podles-Woronowicz, and Watamuraet al. As a commutation algebra, it has the classical form _q ^/* U _q (sl(2, )) U _q (sl(2, )). However, this splitting is not preserved by the coalgebra structure which we also give. For the derivation, we use a generalization of the approach of Sudbery, viz. tangent vectors at the identity.     

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.     

Inverse Problem for a General Bounded Domain inR3 with Piecewise Smooth Mixed BoundaryConditions

We study the influence of a finite container on an ideal gas. The trace of theheat kernel (t) = _{= 1}exp(–t), where {} _{= 1}are the eigenvalues of the negative Laplacian – ² = – ³ _{= 1}(/x )² in the (x ¹, x ², x ³)-space,is studied for a general bounded domain with a smooth bounding surface S, where afinite number of Dirichlet, Neumann, and Robin boundary conditions on thepiecewise smooth parts S _i (i = 1, ..., n) of S are considered such that S =U _{i = 1} S _i . Some geometrical properties of (the volume, the surface area, the meancurvature, and the Gaussian curvature) are determined. Furthermore,thermodynamic quantities, particularly the energy, for an ideal gas enclosed inthe general bounded domain with Dirichlet, Neumann, and Robin conditionsare examined with the help of the asymptotic expansions of (t) for short timet. We show that these thermodynamic quantities depend on some geometricproperties of .     

The effects of inkomogeneous center structure on the shape of the ESR spectra of alkali-rich glasses

The paper considers the effect of nonuniform structure in the centers on the ESR spectrum for the case of axial anisotropy in the g factor; it is shown that if (² >² , _¦ >), the model enables one to describe fairly completely the spectrum of a glass containing 33% Na₂O and 67% SiO₂. Good agreement with all experimental evidence is not obtained for potassium silicate glasses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 86–90, June, 1971.     

Parabolic problems for the Anderson model

The objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics, in particular in hydrodynamics. On a qualitative level, intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments. The paper deals with the Cauchy problem (/t)u(t,x)=Hu(t, x), u(0,x)=t ₀(x) 0, (t, x) ₊ × ^d , for the Anderson HamiltonianH = + (·), (x),x d where is a (generally unbounded) spatially homogeneous random potential. This first part is devoted to some basic problems. Using percolation arguments, a complete answer to the question of existence and uniqueness for the Cauchy problem in the class of all nonnegative solutions is given in the case of i.i.d. random variables. Necessary and sufficient conditions for intermittency of the fieldsu(t,·) ast are found in spectral terms ofH. Rough asymptotic formulas for the statistical moments and the almost sure behavior ofu(t,x) ast are also derived.     

ВЛИЯНИЕ ПРИМЕСЕ Й НА С ВОЙСТВА АНТИМОНИДА И НДИЯ

. — , Ib, IIb, IIIb - , -.