On the long term behavior of some finite particle systems

Summary We consider the problem of comparing large finite and infinite systems with locally interacting components, and present a general comparison scheme for the case when the infinite system is nonergodic. We show that this scheme holds for some specific models. One of these is critical branching random walk onZ ^d . Let _t denote this system, and let _t ^N denote a finite version of _t defined on the torus [–N,N] ^d Z ^d . Ford3 we prove that for stationary, shift ergodic initial measures with density , that ifT(N) andT(N)/(2N+1)^d s[0,] asN, then {v }, 0 is the set of extremal invariant measures for the infinite system _t andQ _s is the transition function of Feller's branching diffusion. We prove several extensions and refinements of this result. The other systems we consider are the voter model and the contact process.Work supported in part by the National Science Foundation under Grant DMS-8802055, by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell University and by the Deutsche Forschungsgemeinschaft through the SFB 123 at the Universität Heidelberg     

Electron Emission from Clean Solid Surfaces by Fast Ions

Total backward electron yields from 27 elemental, non-crystalline, clean solids were measured during bombardment by H⁺-, H-, H-, He⁺- and Ar⁺-ions in the energy range from 100 keV to 800 keV. The yields were found to exhibit an oscillatory dependence on the atomic number of the target material correlated with the periods of the periodic system. These Z₂-oscillations are relatively insensitive to the type of projectile and the impact energy at the high projectile energies of this experiment. Present theories of electron emission cannot explain the main experimental results. The reasons for this failure are discussed.     

Vibrotactile temporal gap detection as a function of age

The ability of subjects to detect temporal gaps between bursts of sinusoids or bursts of bandlimited noise was measured to evaluate the phenomenon of tactile "sensory persistence" in older persons. Vibratory stimuli were delivered to the right thenar eminence of 27 subjects ranging in age from 8-75 years. The subjects' task was to detect the presence of a silent interval or "gap" between flanking 350-ms vibrotactile stimuli. The gap-detection threshold, expressed as the amplitude of vibration relative to the absolute detection threshold, decreased as the gap duration increased and was higher for gaps in noise than for gaps in sinusoids. The threshold for detecting short gaps increased with age for noise stimuli, but not for sinusoidal stimuli. Furthermore, the gap-detection threshold recovered more rapidly in older subjects for noise stimuli, but less rapidly in older subjects for sinusoidal stimuli. Because of these differences, it appears that the effects of age on gap detection cannot be due to a simple increase in sensory persistence, but may be due to multiple processes.     

Random fields and quantum effects in proton glasses

The effects of quantum fluctuations on the proton glass phase in mixed hydrogen-bonded ferro-antiferroelectric systems are considered. The system is described in terms of the infinite-ranged Ising pseudospin glass model in a transverse tunneling field in the presence of random parallel fields. The stability limit of the high-temperature proton glass phase is determined within the thermofield dynamic approach, and the behavior or linear and nonlinear susceptibility is evaluated.     

Spin content of the nucleon in a non-topological chiral soliton model

The spin content of the proton is investigated by studying the flavor singlet axial structure of the nucleon in a non-topological chiral soliton model. In order to construct a nucleon state we used the generator coordinate projection method as well as a coherent state for the meson wave function. Using a standard set of parameters we found the value g _A ⁰ ? 0.44 for the flavor singlet axial vector coupling constant. This result is not far from that of a typical valence quark model.     

Electronic structure and Fermi surface of Bi2Sr2CaCu2O8

Applying angle-resolved photoemission spectroscopy of high angular and energy resolution we have measured the electronic structure of single crystals of Bi₂Sr₂CaCu₂O₈ near the Fermi energy. Along the high symmetry direction X a band is observed to disperse upwards and to cross the Fermi level, whose unoccupied part constitutes the hole-like carriers responsible for the superconductivity. From spectra along the M direction we find evidence for an electron pocket around the M point. The measured band widths appear to be drastically reduced compared with band structure calculations indicating strong electronic correlation effects. From the observation of Fermi-Dirac-like cut-offs in the spectra due to band crossings through the Fermi level we can confirm the existence and, in particular, the shape of the Fermi surface as calculated by band structure calculations.     

Symmetric Markov chains in ℤd: How fast can they move?

Summary Consider a reversible Markov chain X _n which takes values in a subset of ^d. If the steps of the chain are uniformly bounded and the invariant measure satisfies a mild regularity condition, Varopoulos, Carne and Kesten have obtained estimates on \lambda n^{1/2} )$$ " align="middle" border="0"> which exhibit a Gaussian tail in but blow up as n. Following Kesten's approach we derive bounds which are uniform in n in some special cases. Our main result, however, is an example which shows that in general the estimates of Varopoulos, Carne and Kesten are essentially best possible.Research partially supported by an S.E.R.C. (U.K.) visiting fellowship and an operating grant from N.S.E.R.C. of Canada     

Finite sphere packing and sphere covering

A basic problem of finite packing and covering is to determine, for a given number ofk unit balls in Euclideand-spaceE ^d , (1) the minimal volume of all convex bodies into which thek balls can be packed and (2) the maximal volume of all convex bodies which can be covered by thek balls. In the sausage conjectures by L. Fejes Tóth and J. M. Wills it is conjectured that, for alld5, linear arrangements of thek balls are best possible. In the paper several partial results are given to support both conjectures. Furthermore, some relations between finite and infinite (space) packing and covering are investigated.This paper was written while the first named author was visiting the Forschungsinstitut für Geistes- und Sozialwissenschaften at the University of Siegen.     

A renormalization group proof of perturbative renormalizability

This paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean ₄ ⁴ theory. Its aim is partly pedagogical: by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages. The present version is based on the renormalized tree expansion adapted to the continuous renormalization group: all detailed results are proved by induction on the size of the tree. The continuous RG version presented here has one big advantage over the discrete RG version discussed elsewhere. In the continuous version, a tree has a more restrictive structure: there is a one-to-one correspondence between forks of the tree and lines of Feynman graphs. This extra structure eliminates the need to introduce Feynman graphs in the first place. It also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates.Research supported by the Natural Sciences and Engineering Research Council     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.