Semantic incompleteness of quantum physics and EPR-like paradoxes

In the approach to quantum physics (QP) forwarded by the author ana priori formalization of the observative language of the theory is yielded. It is shown here that this formalization allows one to avoid both ontological realism and verificationism, which are the philosophically opposed positions that are usually assumed in the debate on the paradoxes that seem to follow from the analysis of the Einstein, Podolsky, and Rosen (EPR) thought experiment. Some recent results are summarized (in particular, the semantical incompleteness of QP) obtained by the author in the framework of the aforesaid approach, and it is shown that they can be used in order to deal with some EPR-like paradoxes. Thus one can legitimately affirm that at least some of them can be a consequence of semantical ambiguities and of the acceptance of a philosophical dichotomy which is not logically unavoidable.     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interaction that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.     

SDP diagonalizations and perspective cuts for a class of nonseparable MIQP

We present a new approach, requiring the solution of a SemiDefinite Program, for decomposing the Hessian of a nonseparable mixed-integer quadratic problem to permit using perspective cuts to improve its continuous relaxation bound. The new method favorably compares with a previously proposed one requiring a minimum eigenvalue computation.     

Space-time evolution of hadronization in DIS: Semi-exclusive processes and grey track production

Semi-exclusive processes and grey track production in DIS off nuclear targets are analyzed as possible tools to investigate the space time evolution of hadronization.     

BRST cohomology in classical mechanics

The classical (non-quantum) cohomology of the Becchi-Rouet-Stora-Tyutin (BRST) symmetry in phase space is defined and worked out. No group action for the gauge transformations is assumed. The results cover, therefore, the general case of an open algebra and are valid off-shell. Each cohomology class contains all BRST invariant functions with fixed ghost number (an integer) which differ from each other by a BRST variation. If the ghost number is negative there is only the trivial class whose elements are equivalent to zero. If the ghost number is positive or zero there is a bijective correspondence between the BRST classes and those of the exterior derivative along the gauge orbits. These gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish. The BRST invariant functions of ghost numberp are then related to closedp-forms along the orbits. The addition of a BRST variation corresponds to the addition of an exact form. Some comments about the quantum case are included. The physical meaning of the classes with ghost number greater than zero is not discussed.Chercheur qualifié du Fonds National de la Recherche Scientifique (Belgium)     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

The lignol approach to biorefining of woody biomass to produce ethanol and chemicals

Processes that produce only ethanol from lignocellulosics display poor economics. This is generally overcome by constructing large facilities having satisfactory economies of scale, thus making financing onerous and hindering the development of suitable technologies. Lignol Innovations has developed a biorefining technology that employs an ethanol-based organosolv step to separate lignin, hemicellulose components, and extractives from the cellulosic fraction of woody biomass. The resultant cellulosic fraction is highly susceptible to enzymatic hydrolysis, generating very high yields of glucose (>90% in 12–24h) with typical enzyme loadings of 10–20 FPU (filter paper units)/g. This glucose is readily converted to ethanol, or possibly other sugar platform chemicals, either by sequential or simultaneous saccharification and fermentation. The liquor from the organosolv step is processed by well-established unit operations to recover lignin, furfural, xylose, acetic acid, and a lipophylic extractives fraction. The process ethanol is recovered and recycled back to the process. The resulting recycled process water is of a very high quality, low BOD₅, and suitable for overall system process closure. Significant benefits can be attained in greenhouse gas (GHG) emission reductions, as per the Kyoto Protocol. Revenues from the multiple products, particularly the lignin, ethanol and xylose fractions, ensure excellent economics for the process even in plants as small as 100 mtpd (metric tonnes per day) dry woody biomass input—a scale suitable for processing wood residues produced by a single large sawmill.     

A highly specific polyclonal antiserum to the environmental contaminant 1,1,1-trichloro-2,2-bis-(4-chlorophenyl)-ethane (p,p′-DDT)

A very selective polyclonal antiserum against 1,1,1-trichloro-2,2-bis-(4-chlorophenyl)-ethane (p,p′-DDT) was obtained by a careful choice of the haptenic structure (2,2-bis(4-chlorophenyl)-ethanol hemisuccinate). This hapten was conjugated to BSA to prepare the immunogen. The effects of different types of solid phases on the equilibrium reaction between the hapten on solid phase and the polyclonal antiserum were evaluated to obtain a fine tuning of the antiserum performances in terms of specificity for p,p′-DDT and sensitivity to low levels of this pesticide. The calibration curves obtained show that it is possible to set up a sensitive assay for p,p′-DDT, employing a p,p′-dichlorodiphenylacetic acid-based solid phase, with a detection limit of 0.12 ng/mL and a working range of about 0.21–40 ng/mL. Selectivity towards several p,p′-DDT-related substances was good (o,p-DDT 17%, p,p′-DDD 1.2% o,p-DDD 6.3%, p,p′-DDE 6.7%).