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.     

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.     

Constrained random walks and vortex filaments in turbulence theory

We consider a simplified model of vorticity configurations in the inertial range of turbulent flow, in which vortex filaments are viewed as random walks in thermal equilibrium subjected to the constraints of helicity and energy conservation. The model is simple enough so that its properties can be investigated by a relatively straightforward Monte-Carlo method: a pivot algorithm with Metropolis weighting. Reasonable values are obtained for the intermittency dimensionD, a Kolmogorov-like exponent , and higher moments of the velocity derivatives. Qualitative conclusions are drawn regarding the origin of non-gaussian velocity statistics and regarding analogies with polymers and with systems near a critical point.This work was supported in part by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, under Contract Number DE-AC03-76SF000098     

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.     

A goldstone mode in the Kawasaki-Ising model

The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a quantum extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.     

Multivoice Littlewood-Paley-Meyer wavelets and diagonal dominated pseudodifferential operators

Given a pseudodifferential operator (p) satisfying certain growth and smoothness conditions in momentum space, we construct a wavelet basis ofL ²( ^d ) in which the corresponding matrix is diagonal dominated with arbitrarily small prefactor.     

The adiabatic approximation for quantum spin systems with a spectral gap

Summary We estimate the accuracy of the adiabatic approximation in predicting the time evolution of local observables for an XY quantum magnet with a slowly variable external magnetic field. The system evolves according to the natural Hamiltonian dynamics and the spectral gap produced by the magnetic field is assumed to be large with respect to the term inducing quantum fluctutions. The proof is based on a finite order truncation of a time dependent cluster expansion in inverse powers of the time scale . In the analytic case, we show that the accuracy of this truncated expansion is of order for any >1. If the time dependent perturbation is suddenly switched on at time zero and switched off at time , the accuracy of the adiabatic approximation is proven to be of orderO( ^–1.     

Synthesis,characterization and a thermogravimetric study of copper,cobalt and tin mono- and bis-adducts with ethyleneurea,ethylenethiourea and propyleneurea

This paper describes the synthesis, characterization and a thermogravimetric (t.g.) study of 11 adducts of general formula MCl₂·nL (M = Cu, Co and Sn; n = 1 and 2 for Sn, and 2 for Cu and Co; L = ethyleneurea eu, ethylenethiourea etu, and propyleneurea pu). The i.r. results shows that the eu and pu adducts are coordinated through oxygen, whereas for etu nitrogen is the coordination site. The (C=O) or (C=S) trend is: Cu > Co > Sn. The t.g. curves show that the adducts release ligand molecules in a single mass loss step. As regards considering adducts with the same stoichiometry, the observed thermal stability trend is: etu > pu > eu.     

Thermogravimetric determination of magnesium,potassium and lead by precipitation with dilituric acid

The thermolysis curves of magnesium, potassium, and lead diliturate have established that either the hydrated or anhydrous forms of these precipitates are stable enough for their gravimetric use to be possible. Magnesium and lead were determined by precipitation with dilituric acid while potassium was precipitated with trimethylamine diliturate.