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.     

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.     

Meyer's concept of quasicrystal and quasiregular sets

This paper relates two mathematical concepts of long-range order of a set of atoms , each of which is based on restrictions on the set of interatomic distances –. A set in ⁿ is aMeyer set if is a Delone set and there is a finite setF such that . Meyer proposed that such sets include the possible structures of quasicrystals. He obtained a structure theory for such sets, which reformulates results that he obtained in harmonic analysis around 1970, and which relates these sets to cut-and-project sets. In geometric crystallography V.I. Galiulin introduced the concept ofquasiregular set, which is a set such that both and – are Delone sets. This paper shows that these two concepts are identical.     

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.     

Double hypernuclei and the Λ-Λ interaction

The binding energy of the double hypernucleus Be¹⁰ analyzed using an -particle model. A relationship is found between B, the binding energy of two -particlcs, and ¯V, the - potential integral. For the experimental value B = 17.5 Me V ¯V varies from 250 to 850 MeV-F³ according to the form of the - potential used.In conclusion, I wish to thank S. N. Kryuchkova for carrying out these calculations on a Minsk-2 electronic computer. I also wish to thank my senior colleague, V. A. Filimonov, for his support in the completion of the present work.     

Weakly Bound States in Light Hypernuclei

From the viewpoint of critical stability, we discuss the three- and four-body structure of ⁶He, ⁷He, ⁴He, and ⁴H. With the + + N three-body model, ⁶He is found to have a three-layer structure of the matter distribution: core, a skin and neutron halo. Also the level structure of ⁷He with the three-body model of ⁵He + n + n is predicted. This stimulates a new study of neutron-rich and proton-rich hypernuclei. By performing a four-body calculation with both NNN and NNN channels and with both NN and NNN channels, we show that the N-N and -N couplings are very important in critical stability of few-body hypernuclear systems.     

Inertial reference frames in Einstein's theory of gravitation

A physical definition of the inertial reference frame (IRF) is given, and the properties of solutions of the Einstein equation (with cosmological constant), which admit an IRF (IRF solutions) are investigated. Their Petrov type is uniquely determined by the viscous stress tensor. Only the typesI, D or 0 are possible. The unique vacuum IRF solution is the Minkowski space-time. The unique IRF solution belonging to a perfect fluid is the Einstein universe. is of special importance. For=0, the only physically admissible IRF solution is the Minkowski space-time. For0, only interior solutions with strong restrictions for density and pressure are possible.     

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.     

The prediction of the behaviour of Λ-hyperon electromagnetic form factors

The behaviour of the -hyperon electric and magnetic form factors is predicted within the modified three resonance ((783), (1020), (1680)) vector-meson dominance (VMD) model with correct analytic properties and the asymptotic behaviour predestinated by the quark model for baryons. The resonance couplings to are evaluated from the known couplings to nucleons by utilizing theSU(3) symmetry and normalization conditions for Dirac and Pauli form factors. The masses and widths of the considered vector mesons are fixed at the world averaged values. The optimal position of the effective inelastic threshold, common for Dirac and Pauli form factors, is determined from the fit of the only existing Orsay DM2 point on the cross section att=5·693 GeV². The mean square charge and magnetic radii of the -hyperon are found to be r _E ² =0·018 F² and r _M ² =–0·027 F², respectively.The authors are very much indebted to Prof. R. Baldini-Ferroli for calling their attention to the problem of -hyperon e.m. ff 's in connection with the FENICE experiment.     

Nontrivial extensions of a representation of the Poincaré group with mass and helicity zero by its tensorial product

Let U(a, ) be a representation of the Poincaré group with mass and helicity zero, realized in the space of C -functions with compact support on ³, without the origin. Let U ⁽²⁾(a, ) denote the tensorial product of U(a, ) by itself. We explicitly determine the cocycles of extension of U(a, ) by U ⁽²⁾(a, ) and we prove that the nontrivial cohomology is indexed by (u(),),u()D ¹ _]0,3\,.     

An accelerated closed universe

We study a model in which a closed universe with dust and quintessence matter components may look like an accelerated flat Friedmann–Robertson–Walker (FRW) universe at low redshifts. Several quantities relevant to the model are expressed in terms of observed density parameters, _M and , and of the associated density parameter _Q related to the quintessence scalar field Q.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

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.     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

Stability domain of coherent laser waves

The constant-amplitude solutions with wavelength of a semiclassical laser model exhibit three different instabilities in the (, )-plane for pumpparameters above threshold.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Hypernuclear spectroscopy

Conclusions The main difference between the- nucleus and the nucleon-nucleus interaction is in the spin dependence. The spin-spin and spin-orbit interaction is an order of magnitude weaker for the-nucleus than for the nucleon-nucleus system. If we want to emphasize the difference between hypernuclei and nuclei in an oversimplifying manner, we may say that the particle in the nucleus behaves like a spinless neutron.This radical difference in the behaviour of particles and nucleons in nuclear matter presents a sensitive test for the models of nuclear matter. Hypernuclear spectroscopy if studied in detail, a program just begun, promises to give valuable information on the effective properties of the quasiparticles in the nucleus and their interactions, both basic ingredients of nuclear models.Rather surprisingly, hypernuclei live long enough to observe individual states, as can be deduced from the berylium results. These results should be verified as soon as possible. If they are confirmed, this will challenge experimentalists to determine the -nucleus interaction in the same way as done for particles and the theorists to explain why the strong decay of particles in the nucleus is hindered.Invited talk at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

Λ-d Scattering

A three-particle variational calculation of the cross sections and phases of elastic -d scattering in the doublet and quartet states with zero orbital angular momentum is carried out in the energy range from 0 to 20 MeV (laboratory system of coordinates). The calculation is carried out with semirealistic N-N Afnan-Tang potentials and -N potent: —N, which describe -p scattering correctly, as well as the binding energy of the hyperfragments ⁵ He, ¹³ C (within the scope of the + core model), and ³ H (considered as a three-body system).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 114–118, 1981.     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.