Exact parent Hamiltonian for the quantum Hall states in a lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.     

The average a posteriori error of numerical methods

Summary The definition of the average error of numerical methods (by example of a quadrature formula to approximateS(f)= f d on a function classF) is difficult, because on many important setsF there is no natural probability measure in the sense of an equidistribution. We define the average a posteriori error of an approximation by an averaging process over the set of possible information, which is used by (in the example of a quadrature formula,N(F)={(f(a ₁), ...,f/fF} is the set of posible information). This approach has the practical advantage that the averaging process is related only to finite dimensional sets and uses only the usual Lebesgue measure. As an application of the theory I consider the numerical integration of functions of the classF={f:[0,1]/f(x)–f(y)||x–y|}. For arbitrary (fixed) knotsa _i we determine the optimal coefficientsc _i for the approximation and compute the resulting average error. The latter is minimal for the knots . (It is well known that the maximal error is minimal for the knotsa _i .) Then the adaptive methods for the same problem and methods for seeking the maximum of a Lipschitz function are considered. While adaptive methods are not better when considering the maximal error (this is valid for our examples as well as for many others) this is in general not the case with the average error.     

Ring currents in aromatic hydrocarbons

Coupled Hartree-Fock theory is used to compute and map the current density induced in planar hydrocarbons by an external magnetic field. Results of useful accuracy can be obtained with modest (6-31G**) basis sets by employing a continuous gauge transformation. Maps are presented and discussed for benzene, naphthalene, anthracene, tetracene, pentacene, heptacene, and biphenylene. © 1996 John Wiley & Sons, Inc.     

Anionic polymerization of butadiene: A MNDO study of the potential energy surface of the propagation reaction in polar and non-polar media

The anionic polymerization of butadiene, to both the 1,2- and 1,4-addition products, is an important industrial process. It is known that the reaction can be steered to either the 1,2- or 1,4-product by the addition, or absence, of a complexing solvent such as ether. The goals of the current study were to map the MNDO Potential Energy Surfaces (PES) of the propagation reactions both in the presence and absence of dimethyl ether to gain insight into the factors influencing the reaction's selectivity. Single point ab initio calculations at the DZP level were run on all reactants, products and transition states as a cross check on the MNDO results.     

Homometric polytypes

A new theorem on homometric polytypes is presented. Examples of homometric close-packed structures and MX₂-polytypes are given. The method derived may be used to construct homometric n-tuplets by means of decomposition procedures.     

The Duotron,Can It Solve the Solar Neutrino Problem?

At a summary of the four present measurements for the solar neutrino problem one receives for the quotient of the number of the really observed events and the theoretically by the standard solar model exspected value the result This says that in the mean only 33.25% with a possible mistake of 19.25% of the exspected solar neutrinos have been observed. If one goes out from the assumption, that the attempts hitherto proposed for the solution of the problem on the solar neutrino deficits as to be regarded as very unsatisfactory on the one side, while on the other the neutrinos of the β-decay may not exist at all, this looks very troublesome. But there is another possibility of a new interpretation. One has to consider, that in connection with each theoretically until now assumed neutrino of β-decay at the solar p-p- and all joined following fusion -processes precisely one positron will be produced. Exactly this particle will with the probability 1/2 in a triplett state of fixing with an electron of the solar centre plasma at a binding energy of −2029.7 eV create an electric-neutral duotron. This particle assumes fully, inclusive the very welcome factor 1/2, the rǒle of the theoretically dispensable neutrino. This can be regarded as the solution of the solar neutrino-problem.     

Evolution and Trade-Off Dynamics of Functional Load

Functional load (FL) quantifies the contributions by phonological contrasts to distinctions made across the lexicon. Previous research has linked particularly low values of FL to sound change. Here, we broaden the scope of enquiry into FL to its evolution at higher values also. We apply phylogenetic methods to examine the diachronic evolution of FL across 90 languages of the Pama–Nyungan (PN) family of Australia. We find a high degree of phylogenetic signal in FL, indicating that FL values covary closely with genealogical structure across the family. Though phylogenetic signals have been reported for phonological structures, such as phonotactics, their detection in measures of phonological function is novel. We also find a significant, negative correlation between the FL of vowel length and of the following consonant—that is, a time-depth historical trade-off dynamic, which we relate to known allophony in modern PN languages and compensatory sound changes in their past. The findings reveal a historical dynamic, similar to transphonologization, which we characterize as a flow of contrastiveness between subsystems of the phonology. Recurring across a language family that spans a whole continent and many millennia of time depth, our findings provide one of the most compelling examples yet of Sapir’s ‘drift’ hypothesis of non-accidental parallel development in historically related languages.     

Automorphisms of split Cayley algebras over real closed fields

Research supported in part by NSERC Canada grant A7251.     

Numerical simulation of the effect of grain fragmentation on the evolution of microstructure quantities

Meccanica - In this paper the effect of grain fragmentation of a cohesionless granular material on the change of microstructure quantities is investigated using a micropolar continuum model. To...