A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

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.     

Electronic surface states on Pd(110): Theory and comparison with experiment

A relativistic Green function formalism has been applied to calculate layer-projected densities of states on Pd(110). In particular, we obtained unoccupied surface states and their dispersion relations along two directions in the surface Brillouin zone. Good agreement with recent inverse photoemission data is reached by using an energy-dependent dynamical surface potential barrier, which is based on a simple electron-plasmon interaction model, instead of a static surface barrier.     

Antiferromagnetism of type II in nonstoichiometric YbP

A polycrystalline smaple of nonstoichiometric ytterbium phosphide, YbP_0.84, was investigated by neutron scattering, Mössbauer spectroscopy and bulk magnetic measurements. Neutron diffraction experiments prove the existence of antiferromagnetic type II ordering belowT _N =0.64 K, in contrast to the observed antiferromagnetic type III ordering in the stoichiometric Kondo-like compounds YbN and YbAs. The temperature dependence of the average ordered magnetic moment per Yb³⁺ ion with saturation value _Yb = 1.03(7) _B is similar to that of YbN. Mössbauer experiments prove the magnetic phase transition to be first order with different regions in the sample having slightly different transition temperatures. By means of inelastic neutron scattering the crystal-field level scheme was established to be ₆ – ₈(19meV) – ₇(43meV).     

The clinical status of low energy laser therapy in 1989

Low energy laser therapy has gained varying acceptance as a treatment for a broad range of soft tissue, musculoskeletal and neurological conditions. A controversial, but surprisingly large body of research with cell cultures suggests that laser irradiation can nondestructively alter cellular processes. Unfortunately, animal and human studies are often contradictory and difficult to evaluate due to differing study designs. As a result, the clinical effectiveness of low energy laser therapy remains debatable. Nevertheless, the findings are intriguing and deserve further investigation.     

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.     

A Dynamic location problem for graphs

We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a window into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.     

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