Test of the Pauli exclusion principle for nucleons and atomic electrons by accelerator mass spectrometry

The Pauli exclusion principle was tested by searching with accelerator mass spectrometry for non-Paulian atoms with three electrons in theK-shell and for non-Paulian nuclei with three protons or three neutrons in the nuclear 1 s_1/2 shell. For non-Paulian atoms of and the following limits have been obtained: and . For non-Paulian nuclei of and with three protons or three neutrons, respectively, in the nuclear 1 s_1/2 shell the following limits have been measured: for a range of proton separation energies of between 0 and 50 MeV and for neutron separation energies between 0 and 32 MeV. The result for⁵Li is used to deduce a limit for the probability ²/2 of finding two colliding protons in the symmetric state with respect to exchange to be ²/2<>^–32.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday. Supported by the BMFT     

Spectrum of the velocity autocorrelation function of a molecule in a liquid

The theory of the autocorrelation function _V(t) of the velocity of an isolated molecule is formulated, taking into account the contributions of longitudinal and transverse modes of motion. The spectral density function of _V(t) accordingly, turns out to be expressed in terms of two independent susceptibilities, one of the relaxation type and the other of the wave type. The simple dispersion model constructed on the basis of the theory developed in the article agrees very precisely with the data of a computer experiment for liquid argon over the entire range of variation of.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 27–32, August, 1978.     

Ergodic states in a non commutative ergodic theory

Using the Godement mean of positive-type functions over a groupG, we study -abelian systems { , } of aC*-algebra and a homomorphic mapping of a groupG into the homomorphism group of . Consideration of the Godement mean off(g)U _g withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) ( _g (A)) withA and a covariant representation of the system { , } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over . Finally we investigate the discrete spectrum of covariant representations of { , } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma.     

On the massive sine-Gordon equation in the first few regions of collapse

We study the ultraviolet stability problem for the two-dimensional Yukawa interaction :cos:d in the region , where . The results have a natural Coulomb gas interpretation, because the counterterms do not depend on the field.Partially supported by C.N.R.S. trough the University of Paris VI     

A continuum analogue of the lattice gas

We construct a Hilbert space , spanned by vectors , where is a bounded measurable set in ^v (=dimension of space), and interpret as at state where all pointsx are occupied by an incompressible fluid, andx unoccupied. is generated by applying unitary filling operatorsU( ) to a cyclic vector |, the completely unoccupied state. The operatorsU( ) generate a commutativec*-algebra, of which the hermitian elements are interpreted as the observables of the theory.All the -divisible representations of the symmetric group of order 2 are found. We give a generalization to a theory with any number of particle types.     

On the purification of factor states

Let be aC*-algebra and be an opposite algebra. Notions of exact andj-positive states of are introduced. It is shown, that any factor state of can be extended to a pure exactj-positive state of . The correspondence generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states ₁ and ₂ are quasi-equivalent if and only if their purifications and are equivalent.     

Higher spin BRS cohomology of supersymmetric chiral matter inD=4

We examine the BRS cohomology of chiral matter inN=1,D=4 supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators _{(a, b)} are products of the elementary chiral superfieldsS and and the derivative operatorsD , and . Such superfields _{(a, b)} can be chosen to have a symmetrized undotted indices _i and b symmetrized dotted indices . The result derived here is that each composite superfield _(a,b) is subject to potential supersymmetry anomalies ifa–b is an odd number, which means that _(a,b) is a fermionic superfield.     

Quantization of space-time and the corresponding quantum mechanics

An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a canonical quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation [t,r]=±i . The two cases will be considered simultaneously. In that case the event space is the Hilbert space L²(³). Unitary symmetries consist of Poincaré-like symmetries (translations, rotations, and inversion) and of gauge-like symmetries. Space inversion implies time inversion. Thisq space-time reveals a confinement phenomenon: Theq particle is confined in an size region of Minkowski space at any time. One particle mechanics overq space-time provides mass eigenvalue equations for elementary particles. Prugoveki's stochasticq mechanics andq space-time offer a natural way for introducing and interpreting consistently such aq space-time andq particles existing in it. The mass eigenstates ofq particles generate Prugoveki's extended elementary particles. When 0, these particles shrink to point particles and is recovered as the classical (c) limit ofq space-time. Conceptual considerations favor the case [t,r]=+i , and applications in hadron physics give the fit 2/5 fermi/GeV.This paper is a revised version of the author's work, Quantization of Space-time and the Corresponding Quantum Mechanics (Part I), report KFKI-1981-48.     

On the blow-up of solutions of the 3-D Euler equations in a bounded domain

It is shown that if [0, ) is the maximal interval of existence of a smooth solutionu of the incompressible Euler equations in a bounded, simply connected domain R ³, then , where =×u is the vorticity. Crucial to this result is a special estimate proven in of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity.     

Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

Dual moment maps into loop algebras

Moment maps are defined from the space of rank-r deformations of a fixedn xn matrixA to the duals of the positive half of the loop algebras . These maps are shown to give rise to the same invariant manifolds under Hamiltonian flow obtained through the Adler-Kostant-Symes theorem from the rings of invariant functions. This gives a dual characterization of integrable Hamiltonian systems as isospectral flow in the two loop algebras.This research partially funded by NSF grant DMS-8601995, U.S. Army grant DAAL03-87-K-0110, and the Natural Sciences and Engineering Research Council of Canada.     

Logarithmic Sobolev inequality for lattice gases with mixing conditions

Let denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let be the corresponding canonical measure defined by conditioning on . Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed, is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for forall chemical potentials . We prove that for any probability densityf with respect to ; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship.     

On affine yangians

A Yangian , a deformation of the universal enveloping algebra of the two-dimensional loop algebra sl(2) C [t ^–1,t;u], is constructed. This deformation is an analogue of a Yangian which was constructed by V. Drinfeld for any simple Lie algebra. The PBW theorem for is proved and some representations are constructed. Like usual Yangians, possesses a one-dimensional group of auto- morphisms and at zero level - a two-dimensional group of automorphisms. This observation allows one to conjecture that the representation theory of should give rise to new solutions of QYBE.Yangians of other affine algebras can be constructed similarly and they enjoy similar properties.     

Spin-orbit splitting in σ-hypernuclei

The shell model analysis of experimental 0⁺, 2⁺ spectra of and as obtained from (K ^–, ⁺) in-flight and stoppedK ^– reactions, is performed. It suggests a large (twice that for nucleons) spin-orbit splitting of hyperon levelsp _3/2 andp _1/2. Certain constraints on effective central N interaction arise, as well. Some experiments are put forward to further test this value and to extend it to hypernuclei.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Anderson localization for the almost Mathieu equation: II. Point spectrum for λ>2

We prove that for any >2 and a.e. , the pure point spectrum of the almost Mathieu operator (H()) _n = _n-1 + _n+1 + cos(2( +n)) _n contains the essential closure of the spectrum. Corresponding eigenfunctions decay exponentially. The singular continuous component, if it exists, is concentrated on a set of zero measure which is nowhere dense in .     

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.     

The metal-semiconductor transition in amorphous Si1-x Crx films: phenomenological model for the metallic region

A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It was shown in [1] that the cusp-like low-temperature contribution can be described by wherep=0.19±0.03. Starting from this result, two furtherT dependent contributions are separated: The high-temperature region is dominated by a positive contribution _ht (T, x), which is approximately independent ofx, nearly linear inT above 100 K and nearly quadratic inT below 30 K. ForT 4 K, there is a small deviation, increasing withT, from the superposition of the above mechanisms. The relation between , being negative, and theT independent part, , exhibits a singularity, where and=0.68±0.05 –(p–0.19). This singularity should be related to the metal-semiconductor transition, taking place atT _c 0.14. The quantity should be interpreted as minimum metallic conductivity. The limitingT dependences asxx _c +0 agrees quantitatively with that one obtained previously for the activated region,xx _c –0. Extrapolation of the phenomenological model obtained leads to the hypothesis that the interplay of and _ht could be the main origin of the temperature coefficient changing its sign in the Mooijregion, at _tc=0. The model enables several trend predictions concerning the value of _tc=0.     

Kinetics and mechanism of copper fracture due to deformation in surface-active paths

The general kinetic characteristics of copper fracture in the presence of surface-active bismuth-lead baths during creep and elongation under tension are explained. It is shown that the subcritical stage of crack development controls the process, whereupon the effects of stresses , temperature, strain rate , surface energy at the copper-bath interface _SL, and surface energy at the grain boundaries _b on the rate of crack development l/ are analyzed. The basic conclusions are that: a)l/=(–) ( and being constants here); b) the crack development activating energy ) the reduction of energy _b, achieved by intergranular internal adsorption of 0.5% antimony, lowers the value of about 50 times; d) a 30% increase in surface energy _SL reduces the cracking rate 30 times, according to the relation (where A=6 · 10^–15 cm²); and e) .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–15, May, 1976.     

Local properties of equilibrium states and the particle spectrum in quantum field theory

It is shown that in a quantum field theory describing free, scalar particles with masses m _i , i there exist locally normal equilibrium states with finite energy density for all temperature >0 if and only if . This result lends support to the conjecture that the nuclearity criterion proposed by Buchholz and Wichmann is sensitive to the thermodynamical properties of field-theoretic models.     

Symmetry and equilibrium states

Within the general framework ofC*-algebra approach to mathematical foundation of statistical mechanics, we prove a theorem which gives a natural explanation for the appearance of the chemical potential (as a thermodynamical parameter labelling equilibrium states) in the presence of a symmetry (under gauge transformations of the first kind). As a symmetry, we consider a compact abelian groupG acting as *-automorphisms of aC*-algebra (quasi-local field algebra) and commuting (elementwise) with the time translation automorphisms _t of . Under a technical assumption which is satisfied by examples of physical interest, we prove that the set of all extremal _t -KMS states (pure phases) ofG-fixed-point subalgebra (quasi-local observable algebra) of satisfying a certain faithfulness condition is in one-to-one correspondence with the set of all extremalG-invariant _t · _t -KMS states ^– of with varying over one-parameter subgroups ofG (the specification of being the specification of the chemical potential), where the correspondence is that the restriction of ^– to is .