Diffractive dissociation reaction np → Λ0K0p for incident neutron momenta between 30 and 70 GeV/c BIS-2 collaboration

We present results of the exclusive diffractive reaction np ⁰K⁰p at 0·08 < |t|< 0·53 GeV²/c² and momenta between 30–70 GeV/c at the Serpukhov neutron beam. Thet-dependence is exp (Bt) withB= 11·4± 2·3 (GeV/c)^–2 and it exhibits the diffractive minimum at ¦t¦ 0·28 GeV²/c² for ⁰K⁰ massesM < 1·8 GeV/c².B decreases with increasingM. Correlation with the beam direction is observed in the rest frame of the ⁰K⁰ system: the cross section rises for the forward-going ⁰. The rise is more pronounced for higherM. The cross section of reaction np ⁰K⁰p for 0<|t|< 0·53 GeV²/c² is 10·3 ± 2·5 ± 2·8 b.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains

We study the integrated density of statesH( ²) of a chain of harmonic oscillators with a binary random distribution of the masses. We show in particular that there is a dense set of values of the squared frequency for which the differenceH( ²+)-H( ²) has a singularity of the type ¦¦², multiplied by a periodic function of ln ¦¦, where the exponent and the period depend continuously on ². In the region where < 1/2,H is not differentiate on a dense set of points. The same type of singularities is also present in the Lyapunov coefficient.     

On the time evolution automorphisms of the CCR-algebra for quantum mechanics

In ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form is studied from the point of view of *-automorphisms of the CCRC*-algebra (see Ref. [1, 2]). It is proved that those Hamiltonians do not induce *-automorphisms of this algebra in the cases: a) and b)V L (,dx) L ¹ (,dx), except when the potential is trivial.     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

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.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

Magnetic moments of nuclei around146Gd

Nuclear orientation measurements down to 2.5 mK have been performed on implanted sources of¹⁴⁶Eu,¹⁴⁷Gd and¹⁴⁹Gd in iron. Using a two site model interaction frquencies were deduced from the data. From these, ratios of magnetic moments have been derived as ¦(¹⁴⁸Eu)/(¹⁴⁶Eu)¦=1.90±0.20 and ¦(¹⁴⁹Gd)/(¹⁴⁷Gd)¦=0.86±0.05.     

On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

Special frequencies and Lifshitz singularities in binary random harmonic chains

We consider a one-dimensional chain of coupled harmonic oscillators; the mass of each atom is a random variable taking only two values (M or 1). We investigate the integrated density of statesH(²) near special frequencies: a given frequency _s with rational wavelength becomes special if the mass ratioM exceeds a certain critical valueM _c . We show thatH has essential singularities of the typesH _sg exp(–C ₁ ¦²– _s ² ¦^–1/2) or exp(–C ₂¦²– _s ² ¦^–1), according to the value ofM and the sign of (²– _s ² ). The Lifshitz singularity at the band edge is analyzed in the same way. In each case, the constantC ₁ orC ₂ is evaluated explicitly and compared with a vast amount of numerical work. All these exponential singularities are modulated by periodic amplitudes. The properties of the eigenfunctions with frequencies close to the special values are also discussed, and are illustrated by numerical data.     

Gravitational collapse with charge and small asymmetries I. Scalar perturbations

A recent analysis by Richard Price of spherical collapse with small nonspherical perturbations is here generalized to the case of an electrically charged collapsing star (0¦Q¦-M). The perturbations are confined to a scalar field generated by a nonspherical distribution of scalar charge in the star. As in the electrically neutral case, the scalar perturbations are probably a prototype for all others — electromagnetic, gravitational, and higherspin. The collapse is shown to produce a Reissner-Nordström black hole, and the scalar-field perturbations are shown to radiate completely away; but they die out more slowly the larger is the star's electric charge. For charge ¦Q¦M, the -pole part of the perturbation at fixedr and late times is dominated by a tail that dies out ast ^{–(2+ 2)}. But for ¦Q¦=M, the primary outgoing waves emitted from the star's surface are everywhere larger than the tail. At fixedr and late times they die as t^–(+2). Also, a calculation of the redshift shows that a collapsing star becomes black more slowly the larger is the star's electric charge.Supported in part by the National Science Foundation (GP-27304, GP-28027, GP-19887).     

The charge fluctuations in classical Coulomb systems

We study the asymptotic behavior of the charge fluctuations (Q – (Q )² in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge fluctuations are not extensive, then they are necessarily of the order of the surface ¦¦. Moreover, when the canonical sum rules that are typical for equilibrium states of particles interacting with long-range forces hold true, we prove a central limit theorem for the normalized charge variable ¦¦^–1/2((Q – (Q )) in two and three dimensions. In one dimension, the probability distribution of the charge itself converges. The latter case is illustrated by the example of the one-dimensional Coulomb gas.     

Electrovac fields with geodesic eigenrays

The stationary states of electrovac fields for which the geodesic eigenrays of both the Maxwell and gravitational field coincide are investigated. The fact that the Kerr-Newman solutions belong to this class lends physical interest to the fields considered here. Particular attention is devoted to fields with shearing eigenrays since principal null congruences do not coincide with eigenrays in this case, and so earlier approaches to the problem fail. By the generalisation of a theorem on the corresponding vacuum case, it is proven that no spherical solutions exist in the shearing class, with the exception of the fields with ²¦G_O¦²-¦H_O¦²=O.The metrics with O, admitted by the theorem, can either be calculated from the corresponding vacuum solutions by a relatively simple procedure, or, if not, we list them explicitly in this paper.     

The tortuosity of occupied crossings of a box in critical percolation

We consider the length of an occupied crossing of a box of size [0,n]×[0, 3n] ^D–1 (in the short direction) in standard (Bernoulli) bond percolation on ^D at criticality. Let ¦s _n¦ be the length of the shortest such crossing. It is believed that ¦s _n¦ ^1+c in some sense for somec>0. Here we show that if the correlation length(p) satisfies (p)p _c}–p) ^– for some <1, then with a probability tending to 1, ¦s _n¦>/C ₁ n ^1/(logn)^–(1–)/. The assumption (p)C ₃(p _c–p)^– with <1 has been rigorously established^(1,2) for largeD, but cannot hold⁽³⁾ forD=2. In the latter case, let ¦l _n¦ be the length of the lowest occupied crossing of the square [0,n]². We outline a proof ofP _pc(¦l_n¦ n ^1+c)n ^– for somec, >0. We also obtain a result about the length of optimal paths in first-passage percolation.     

Large charge fluctuations in classical Coulomb systems

The typical fluctuation of the net electric chargeQ contained in a subregion of an infinitely extended equilibrium Coulomb system is expected to grow only as S, whereS is the surface area of. For some cases it has been previously shown thatQ/S has a Gaussian distribution as ¦¦. Here we study the probability law for larger charge fluctuations (large-deviation problem). We discuss the case when both ¦¦ andQ are large, but now withQ of an order larger than S. For a given value ofQ, the dominant microscopic configurations are assumed to be those associated with the formation of a double electrical layer along the surface of. The probability law forQ is then determined by the free energy of the double electrical layer. In the case of a one-component plasma, this free energy can be computed, for large enoughQ, by macroscopic electrostatics. There are solvable two-dimensional models for which exact microscopic calculations can be done, providing more complete results in these cases. A variety of behaviors of the probability law are exhibited.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

The quasilinear theory of two-stream cyclotron instability of electron beams

The paper is devoted to a study of cyclotron instability ( _e) of two opposite beams of electrons from the aspect of the quasilinear effects. For this case of instability the authors evolve the diffusion equation in the velocity space for an averaged distribution function. They estimate the relaxation times , _z of the spreading of the distribution function in the velocity space. At the end of the paper, they compare their results with an experiment described by M. Seidl and P. unka [Phys. Letters11 (1964), 31].     

Scaling solutions of Smoluchowski's coagulation equation

We investigate the structure of scaling solutions of Smoluchowski's coagulation equation, of the formc _k (t)s(t)^– (k/s(t)), wherec _k (t) is the concentration of clusters of sizek at timet,s(t) is the average cluster size, and(x) is a scaling function. For the rate constantK(i, j) in Smoluchowski's equation, we make the very general assumption thatK(i, j) is a homogeneous function of the cluster sizesi andj:K(i,j)=a ^– K(ai,aj) for alla>0, but we restrict ourselves to kernels satisfyingK(i, j)/j0 asj. We show that gelation occurs if>1, and does not occur if1. For all gelling and nongelling models, we calculate the time dependence ofs(t), and we derive an equation for(x). We present a detailed analysis of the behavior of(x) at large and small values ofx. For all models, we find exponential large-x behavior: (x)A x ^– e ^–x asx and, for different kernelsK(i, j), algebraic or exponential small-x behavior: (x)Bx ^– or (x)=exp(–Cx ^–|| + ...) asx0.