The many faces of a character

We prove an identity between three infinite families of polynomials which are defined in terms of bosonic, fermionic, and one-dimensional configuration sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-ansatz solution of the Heisenberg spin chain.     

The many faces of radiation‐induced changes

During diffraction experiments even cryo‐cooled protein crystals can be significantly damaged due to chemical and physical changes induced by absorbed X‐ray photons. The character and scale of the observed effects depend strongly on the temperature and the composition of crystals. The absorption of radiation energy results in incremental regular changes to the crystal structure, making its impact on the process of solving the structure strongly correlated with other experimental variables. An understanding of all the dependencies is still limited and does not allow for a precise prediction of the outcome of a particular diffraction experiment. Results are presented of diffraction experiments performed under different experimental conditions. The influence of temperature and crystal composition on different characteristics of radiation damage is analyzed. The observed effects are discussed in terms of their impact on data processing and phasing procedures.     

Ocneanu cell calculus and integrable lattice models

We show that cell calculus (first introduced by Ocneanu in the context of relative position of factors) is a technique which permits us to connect different integrable models. It generalizes the Vertex-IRF correspondence.     

The many faces of <Emphasis Type="Italic">nano</Emphasis> in newspaper reporting

The morpheme nano in languages such as Swedish and English is a constituent of many words. This article linguistically analyses the meaning potential of nano by focusing on word use in a Swedish newspaper corpus comprising 2,564 articles (1.6 million words) covering a 22-year period (1988–2010). Close to 400 word forms having nano as a constituent have been identified and analyzed. The results suggest that nano covers a broad and heterogeneous conceptual field: (i) as a prefix of the SI system; (ii) in relation to the scientific activities of nanoscience and nanotechnology, including their sub-processes and actors; and (iii) in relation to objects. The identified meanings of nano, besides the standard definition (i.e. ‘billionth part’ in relation to SI units), are ‘operating at the nanometre level’ in relation to activities and their actors and ‘nanometre sized’ and ‘nanotechnological’ in relation to objects; in addition, the less precise and non-technical meaning ‘very small’ is identified. We discuss the implications of the findings for a hypothesis about media influence on public understanding of technology, suggesting that repeated findings in Europe and the USA of little self-reported understanding and knowledge of nanotechnology or nanoscience among the public make sense in light of the polysemy of nano reflected in its broad variety of verbal forms and usages.     

The world of many worlds

The efficient conversion of electrical power from AC to DC is one of the most important problems in electrical technology. The ideal rectifier will present a short circuit path to current flowing in one direction, and an open circuit in the opposite direction. All practical rectifiers have a finite resistance in the conducting or forward direction and measurable leakage in the blocking or reverse direction; further, they all cease to block at all beyond a certain voltage. There is always a certain temperature for each type of rectifier above which its efficiency drops rapidly. The most important features of any rectifier are therefore:     

Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries

For every ADE Dynkin diagram, we give a realization, in terms of usual fusion algebras (graph algebras), of the algebra of quantum symmetries described by the associated Ocneanu graph. We give explicitly, in each case, the list of the corresponding twisted partition functions.     

The many vacua of gauged extended supergravities

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D ≥ 3 scalar potential—that of SO(8) × SO(8) gauged Chern–Simons Supergravity in D = 3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model.     

The electronic work function of the different faces of tungsten

We present a semi-empirical theory of the electronic work function of the different faces of tungsten. All the parameters entering the theory, except one, are estimated independently. The one adjustable parameter relates to the isotropic contribution to the work function, and, can, in principle, be determined from a self-consistent calculation of the band-structure of the energy levels in the bulk of the metal. The calculated values for the work function are in reasonably good agreement with available experimental data for practically all of the crystallographic planes with the exception of the (100) plane. For the latter, the calculated value is 0.3 eV above the experimental value. It is suggested that a negative contribution to the surface dipole potential from surface states, that exist on this plane, may be the reason of this discrepancy.     

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

The Klein paradox as a many particle problem

In this paper we give a mathematically rigorous analysis of the Klein paradox in the many-particle formulation of the Dirac theory. This paradox was meant as an example demonstrating the negative energy problems of the single particle Dirac equation. However, we show that this problem does not disappear in the second quantized version of the Dirac theory. It corresponds with a situation which cannot be described properly within the framework of a field theory with an external potential.     

Nambu dynamical system: The case of many triplets

A modification of the exterior calculus is presented to avoid the vanishing of the square of the canonical 3-form. Once this is done, powers of the canonical 3-form are different from zero up to the volume form. All powers of the canonical 3-form are invariant under the Nambu vector field; this is also valid for the integral of each of these forms. The Darboux theorem is exhibited. A specific realization is constructed.     

The partition function of an interacting many body system

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuations and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. Received 28 March 2002 Published online 17 September 2002     

The adsorption of activated nitrogen on platinum single crystal faces

The adsorption of activated nitrogen on a stepped Pt(S)-[9(111) × (111)] face was investigated by LEED, AES and flash desorption. Nitrogen was supplied to the crystal from a high frequency discharge tube. For comparison some orienting measurements were also carried out on smooth (111) and (100) platinum faces. Activated nitrogen is adsorbed at room temperature on all three faces up to about half a monolayer coverage. No additional LEED patterns indicating long range order of the adsorbed layer were found. By flash heating a small desorption peak at 120°C and a large peak between 175 and 230°C depending on the initial coverage were observed on the (111) type faces. The desorption can be described approximately by a second order rate law with an energy of activation of 25± 3 kcal/mole. No influence of surface steps on the properties of the adsorbed layer was detected. On the (100) face two coverage independent desorption maxima at 120 and 170°C of about equal intensities were found.     

The classical mechanics of one-dimensional systems of infinitely many particles

We apply the existence theorem for solutions of the equations of motion for infinite systems to study the time evolution of measures on the set of locally finite configurations of particles. The set of allowed initial configurations and the time evolution mappings are shown to be measurable. It is shown that infinite volume limit states of thermodynamic ensembles at low activity or for positive potentials are concentrated on the set of allowed initial configurations and are invariant under the time evolution. The total entropy per unit volume is shown to be constant in time for a large class of states, if the potential satisfies a stability condition.On leave from: Department of Mathematics, University of California, Berkeley, California.     

The classical mechanics of one-dimensional systems of infinitely many particles

We prove a global existence and uniqueness theorem for solutions of the classical equations of motion for a one-dimensional system of infinitely many particles interacting by finite-range two-body forces which satisfy a Lipschitz condition.     

The diffusion of interacting classical particles as a many boson problem

We discuss the connection between anN-particle Smoluchowski equation and the quantum mechanical problem of interacting bosons. It is shown that certain correlation functions like, for example, the dynamic structure factor can be expressed as ground state expectation values in the boson system. As an application we calculate the diffusion constant of a system of interacting Brownian particles to second order in the interaction.     

The solutions of the classical KMS-equation for infinitely many non-interacting particles

The complete solution of the classical KMS-equation for quasi-free evolutions is given under two different conditions.