Progress in metric-affine gauge theories of gravity with local scale invariance

Einstein's general relativity theory describes very well the gravitational phenomena in themacroscopic world. In themicroscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for arenormalizable field theory. We argue that thelocal extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to aGL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status ofindependent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein's GR surfaces as an effective low-energy theory.Based on a plenary talk given by one of us (EWM) at the 53rd annual meeting of the Deutsche Physikalische Gesellschaft in Bonn on March 14, 1989.Supported by the German-Israeli Foundation for Scientific Research and Development (GIF), Jerusalem and Munich.Supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, project He 528/12-1.Supported in part by DOE Grant DE-FG05-85-ER40200.     

The absolute order of a permutation representation of a Coxeter group

A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.     

Cellulose Nanocrystals (CNCs) Induced Crystallization of Polyvinyl Alcohol (PVA) Super Performing Nanocomposite Films

This study is aimed to explore the properties of cellulose nanocrystals (CNC)/polyvinyl alcohol (PVA) composite films with and without 1,2,3,4‐butane tetracarboxylic acid (BTCA), a nontoxic crosslinker. CNC and CNC‐PVA nanocomposite films are prepared using solution‐casting technique. Differential scanning calorimetry (DSC) analyses show that crosslinking increased the glass transition temperature but reduced the melting temperature and crystallinity. Furthermore, high CNC concentrations in the PVA matrix interfere with PVA crystallinity, whereas in specific ratio between CNC and PVA, two different crystalline structures are observed within the PVA matrix. Film surfaces and fracture topographies characterized using scanning electron microscope indicate that at certain CNC‐PVA ratios, micron‐sized needle‐like crystals have formed. These crystalline structures correlate with the remarkable improvement in mechanical properties of the CNC‐PVA nanocomposite films, that is, enhanced tensile strain and toughness to 570% and 202 MJ m^?3, respectively, as compared to pristine PVA. BTCA enhances the tensile strain, ultimate tensile stress, toughness, and modulus of CNC films compared to pristine CNC films. Water absorption of crosslinked CNC and CNC‐PVA nanocomposite films is significantly reduced, while film transparency is significantly improved as a function of PVA and crosslinker content. The presented results indicate that CNC‐PVA nanocomposite films may find applications in packaging, and though materials applications.     

Adhesion and stable low friction provided by a subnanometer-thick monolayer of a natural polysaccharide

Using a surface forces apparatus, we have investigated the adhesive and lubrication forces of mica surfaces separated by a molecularly thin, subnanometer film of a high-molecular-weight (2.3 MDa) anionic polysaccharide from the algae Porphyridium sp. adsorbed from aqueous solution. The adhesion and friction forces of the confined biopolymer were monitored as a function of time, shearing distance, and driving velocity under a large range of compressive loads (pressures). Although the thickness of the dilute polysaccharide was <1 nm, the friction was low (coefficient of friction = 0.015), and no wear was ever observed even at a pressure of 110 atm over 3 decades of velocity, so long as the shearing distances were less than twice the contact diameter. Atomic force microscopy in solution shows that the biopolymer is able to adsorb to the mica surface but remains mobile and easily dragged upon shearing. The adhesion (adsorption) of this polysaccharide even to negatively charged surfaces, its stable low friction, its robustness (high-load carrying capacity and good wear protection), and the weak (logarithmic) dependence of the friction force on the sliding velocity make this class of polyelectrolytes excellent candidates for use in water-based lubricant fluids and as potential additives to synovial fluid in joints and other biolubricating fluids. The physical reasons for the remarkable tribological properties of the ultrathin polysaccharide monolayer are discussed and appear to be quite different from those of other polyelectrolytes and proteins that act as thick "polymer brush" layers.     

Silicon/molecule interfacial electronic modifications

Electronic structures at the silicon/molecule interface were studied by X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, inverse photoemission spectroscopy, and Kelvin probe techniques. The heterojunctions were fabricated by direct covalent grafting of a series of molecules (-C6H4-X, with X = NMe2, NH2, NO2, and Mo6 oxide cluster) onto the surface of four types of silicon substrates (both n- and p-type with different dopant densities). The electronic structures at the interfaces were thus systematically tuned in accordance with the electron-donating ability, redox capability, and/or dipole moment of the grafted molecules. The work function of each grafted surface is determined by a combination of the surface band bending and electron affinity. The surface band bending is dependent on the charge transfer between the silicon substrate and the grafted molecules, whereas electron affinity is dependent on the dipole moment of the grafted molecules. The contribution of each to the work function can be separated by a combination of the aforementioned analytical techniques. In addition, because of the relatively low molecular coverage on the surface, the contribution from the unreacted H-terminated surface to the work function was considered. The charge-transfer barrier of silicon substrates attached to different molecules exhibits a trend analogous to surface band bending effects, whereas the surface potential step exhibits properties analogous to electron affinity effects. These results provide a foundation for the utilization of organic molecule surface grafting as a means to tune the electronic properties of semiconductors and, consequently, to achieve controllable modulation of electronic characteristics in small semiconductor devices at future technology nodes.     

Interfacial characterization of chemical solution‐deposited thin films of PbSe on GaAs(100)

The microstructure and composition of the interfacial layer between chemically deposited PbSe and GaAs substrates were studied using high‐resolution transmission electron microscopy (HRTEM), Auger electron spectroscopy (AES), x‐ray photoelectron spectroscopy (XPS) and energy‐filtered TEM. The thickness of the interfacial layer varied significantly from direct contact of the film with the substrate to 5 nm in the thickest regions. The results established the presence of a discontinuous, amorphous intermediate layer of Ga₂O₃ at the PbSe/GaAs interface. Copyright © 2008 John Wiley & Sons, Ltd.     

Ultrafast proton transfer of three novel quinone cyanine photoacids

Steady-state and time-resolved emission techniques were used to study the photoprotolytic properties of three recently synthesized strong quinone cyanine photoacids (QCy7 and its sulfonated derivatives). The rate coefficient of the excited-state proton transfer (ESPT), k(PT), of the three dyes is roughly 1.5 × 10(12) s(-1), a high value that is comparable to the solvation dynamics rate of large polar organic molecules in H(2)O and D(2)O. It is twice as fast as the proton transfer rate between two adjacent water molecules in liquid water. We found that, as expected, two of the sulfonated photoacids geminately recombines with the proton at an elevated rate. The accelerated geminate recombination process of the sulfonated derivatives is different from a simple diffusion process of protons. The ESPT rate coefficient of these molecules is the highest recorded thus far.     

A quantum dot close to Stoner instability: The role of the Berry phase

The physics of a quantum dot with electron–electron interactions is well captured by the so called “Universal Hamiltonian” if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close to the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].     

Ruderman-Kittel-Kasuya-Yosida and magnetic-field interactions in coupled Kondo quantum dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].