Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

Linking numbers in local quantum field theory

Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge-invariant) vector potentials, integrated about spacelike separated, spatial loops, are elements of the center of the algebra of all local fields. Moreover, these commutators are proportional to the linking numbers of the underlying loops. If the commutators are different from zero, the underlying two-forms are not exact (i.e. there do not exist local vector potentials for them). The theory then necessarily contains massless particles. A prominent example of this kind, due to J.E. Roberts, is given by the free electromagnetic field and its Hodge dual. Further examples with more complex mass spectrum are presented in this article.

     

Dry Reforming of Methane on a Highly‐Active Ni‐CeO2 Catalyst: Effects of Metal‐Support Interactions on C−H Bond Breaking

Ni‐CeO₂ is a highly efficient, stable and non‐expensive catalyst for methane dry reforming at relative low temperatures (700 K). The active phase of the catalyst consists of small nanoparticles of nickel dispersed on partially reduced ceria. Experiments of ambient pressure XPS indicate that methane dissociates on Ni/CeO₂ at temperatures as low as 300 K, generating CH_x and CO_x species on the surface of the catalyst. Strong metal–support interactions activate Ni for the dissociation of methane. The results of density‐functional calculations show a drop in the effective barrier for methane activation from 0.9 eV on Ni(111) to only 0.15 eV on Ni/CeO_2?x(111). At 700 K, under methane dry reforming conditions, no signals for adsorbed CH_x or C species are detected in the C 1s XPS region. The reforming of methane proceeds in a clean and efficient way.     

Extending the coordination chemistry of 1,3,5-triaza-7-phosphaadamantane (PTA) to cobalt centers: first examples of co-PTA complexes and of a metal complex with the PTA oxide ligand

Water-soluble Co (III) and Co (II) complexes with P- or N-coordinated PTA or PTA oxide ligands, respectively, have been prepared and fully characterized, constituting the first examples of cobalt compounds bearing PTA or any ligand with a cage-like PTA core, the latter complex providing also the first PTA oxide coordination to a metal center.     

Rydberg states with quantum Monte Carlo

Calculations on Rydberg states are performed using quantum Monte Carlo methods. Excitation energies and singlet-triplet splittings are calculated for two model systems, the carbon atom (3P and 1P) and carbon monoxide ((1Sigma and 3Sigma). Kohn-Sham wave functions constructed from open-shell localized Hartree-Fock orbitals are used as trial and guide functions. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method depends strongly on the wave function's nodal hypersurface. Nodal artefacts are investigated for the ground state of the carbon atom. Their effect on the FN-DMC results can be analyzed quantitatively. FN-DMC leads to accurate excitation energies but to less accurate singlet-triplet splittings. Variational Monte Carlo calculations are able to reproduce the experimental results for both the excitation energies and the singlet-triplet splittings.     

Investigations of the catalytic properties of manganese oxides for the oxygen reduction reaction in alkaline media

The oxygen reduction reaction (ORR) was studied in KOH electrolyte on different manganese oxides, dispersed on a carbon powder (MnO_x/C). The oxides were prepared by different methods, for producing MnO, Mn₃O₄ and MnO₂ as major phases dispersed on the Vulcan XC-72 carbon. The oxides were characterized by XRD (X-ray diffraction) and in situ XANES (X-ray absorption near edge structure). The electrochemical measurements were made using cyclic voltammetry and steady state polarization curves carried out in an ultra-thin layer rotating ring/disk electrode. The results have shown lower activity for the ORR on the MnO_x/C species compared to that on Pt/C, but higher activity compared to that of pure Vulcan carbon. Formation of involving 2e⁻ per O₂ molecule is the main path of the ORR in the studied MnO_x/C catalysts but, at low overpotentials and rotation rates the number of electrons is raised to 4 due to the occurrence of a disproportionation reaction. Large differences of electrocatalytic activity were seen for the different oxide species, and these were related to the presence of a Mn(IV) phase and the occurrence of a mediation processes involving the reduction of Mn(IV) to Mn(III), followed by the electron transfer of Mn(III) to oxygen.     

Organocatalytic asymmetric 5-hydroxyisoxazolidine synthesis: a highly enantioselective route to beta-amino acids

The highly chemo- and enantioselective organocatalytic tandem reaction between N-protected hydroxyl amines and alpha,beta-unsaturated aldehydes is presented; the reaction provides access to 5-hydroxyisoxazolidines and beta-amino acids in high yields and with 90-99% ee.     

Sequential gold-catalyzed reactions of 1-phenylprop-2-yn-1-ol with 1,3-dicarbonyl compounds

A variety of sequential gold-catalyzed reactions of 1-phenylprop-2-yn-1-ol with 1,3-dicarbonyl compounds are directed towards different outcomes by a suitable choice of the catalytic system, feature of 1,3-dicarbonyl and reaction conditions.     

Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles

Stretching experiments on single molecules of arbitrary length opened the way for studying the statistical mechanics of small systems. In many cases in which the thermodynamic limit is not satisfied, different macroscopic boundary conditions, corresponding to different statistical mechanics ensembles, yield different force-displacement curves. We formulate analytical expressions and develop Monte Carlo simulations to quantitatively evaluate the difference between the Helmholtz and the Gibbs ensembles for a wide range of polymer models of biological relevance. We consider generalizations of the freely jointed chain and of the worm-like chain models with extensible bonds. In all cases we show that the convergence to the thermodynamic limit upon increasing contour length is described by a suitable power law and a specific scaling exponent, characteristic of each model.     

Copper(II) complexes of bis(amino amide) ligands: effect of changes in the amino acid residue

A family of ligands derived from bis(amino amides) containing aliphatic spacers has been prepared, and their protonation and stability constants for the formation of Cu(2+) complexes have been determined potentiometrically. Important differences are associated to both the length of the aliphatic spacer and the nature of the side chains derived from the amino acid. In general, ligands containing aliphatic side chains display higher basicities as well as stability constants with Cu(2+). In the same way, basicities and stability constants tend to increase when decreasing the steric hindrance caused by the corresponding side-chain. FT-IR, UV-vis and ESI-MS were used for analyzing the complex species detected in the speciation diagram. UV-vis studies showed the presence of different coordination environments for the copper(II) complexes. Complexes with different stoichiometries can be formed in some instances. This was clearly highlighted with the help of ESI-MS experiments.