Concrete Semantics with Coq and CoqHammer

The "Concrete Semantics" book gives an introduction to imperative programming languages accompanied by an Isabelle/HOL formalization. In this paper we discuss a re-formalization of the book using the Coq proof assistant. In order to achieve a similar brevity of the formal text we extensively use CoqHammer, as well as Coq Ltac-level automation. We compare the formalization efficiency, compactness, and the readability of the proof scripts originating from a Coq re-formalization of two chapters from the book

Ising t-J model close to half filling: A Monte Carlo study

Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z_2 symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J_z model, the global SU(2) invariance is fully restored at J_z=0, so that only the spin-spin interaction has in that model the true Ising form. We discuss a relationship between those two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share the qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J_z one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10^3 sites. Within this model we discuss in detail the destruction of the antiferromagnetic order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next nearest neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no double occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.Comment: 24 pages, 10 figure

Hofstadter butterfly for a finite correlated system

We investigate a finite two-dimensional system in the presence of external magnetic field. We discuss how the energy spectrum depends on the system size, boundary conditions and Coulomb repulsion. On one hand, using these results we present the field dependence of the transport properties of a nanosystem. In particular, we demonstrate that these properties depend on whether the system consists of even or odd number of sites. On the other hand, on the basis of exact results obtained for a finite system we investigate whether the Hofstadter butterfly is robust against strong electronic correlations. We show that for sufficiently strong Coulomb repulsion the Hubbard gap decreases when the magnetic field increases.Comment: 7 pages, 5 figures, revte

Time-resolved small-angle x-ray scattering studies during aqueous emulsion polymerization

The persulfate-initiated aqueous emulsion polymerization of 2,2,2-trifluoroethyl methacrylate (TFEMA) is studied by time-resolved small-angle X-ray scattering (SAXS) at 60 °C using a stirrable reaction cell. TFEMA was preferred to styrene because it offers much greater X-ray scattering contrast relative to water, which is essential for sufficient temporal resolution. The evolution in particle size is monitored by both in situ SAXS and ex situ DLS in the absence or presence of an anionic surfactant (sodium dodecyl sulfate, SDS). Post-mortem SAXS studies confirmed the formation of well-defined spherical latexes, with volume-average diameters of 353 ± 9 nm and 68 ± 4 nm being obtained for the surfactant-free and SDS formulations, respectively. 1H NMR spectroscopy studies of the equivalent laboratory-scale formulations indicated TFEMA conversions of 99% within 80 min and 93% within 60 min for the surfactant-free and SDS formulations, respectively. Comparable polymerization kinetics are observed for the in situ SAXS experiments and the laboratory-scale syntheses, with nucleation occurring after approximately 6 min in each case. After nucleation, scattering patterns are fitted using a hard sphere scattering model to determine the evolution in particle growth for both formulations. Moreover, in situ SAXS enables identification of the three main intervals (I, II, and III) that are observed during aqueous emulsion polymerization in the presence of surfactant. These intervals are consistent with those indicated by solution conductivity and optical microscopy studies. Significant differences between the surfactant-free and SDS formulations are observed, providing useful insights into the mechanism of emulsion polymerization

Initial growth of Ba on Ge(001): An STM and DFT study

An ordered alkaline-earth submonolayer on a clean Si(001) surface provides a template for growth of the atomically sharp, crystalline Si-oxide interface that is ubiquitous in the semiconductor device industry. It has been suggested that submonolayers of Sr or Ba on Ge(001) could play a similar role as on structurally identical Si(001), overcoming known limitations of the Ge(001) substrate such as amorphization of its oxidation layers. In this paper the initial stage of the Ba oxidation process, i.e., adsorption and organization of Ba atoms on the Ge(001) surface as a function of temperature (270−770 K) for coverage 1.0 monolayer (ML) and 0.15−0.4 ML, is studied using scanning tunneling microscopy (STM) and density functional theory (DFT). Three types of features have been identified on the Ba-covered Ge(001) surface. They originate from isolated Ba adatoms, isolated Ba ad-dimers, and the Ba ad-dimers assembled into short-range, randomly distributed chains that run across the Ge dimer rows. We find from both STM measurements and DFT calculations that the latter is the dominant structure on Ge(001) with increasing coverage

Higher order reconstructions of the Ge(001) surface induced by a Ba layer

Structural properties of Ba-induced reconstructions on a Ge(001) surface, based on atomic-resolution ultra high-vacuum scanning tunneling microscopy measurements, are discussed. It is shown that while the Ba - Ge layer, which fully covers the surface, is dominated by a phase with an internal 2 × 3 periodicity, it also includes portions of higher order 2 × 6 and 4 × 3 surface reconstructions, always accompanied by 1D protrusions embedded into the dominating phase. Modelling the observed higher order structures, using the elementary cell of the 2 × 3 phase calculated within the density functional theory, is shown to reproduce the experimental data very well. As such the higher order reconstructions can be treated as local defects of the dominating 2 × 3 phase

STM and DFT study on formation and characterization of Ba-incorporated phases on a Ge(001) surface

We characterize the incorporation of Ba adatoms into the Ge(001) surface, resulting in the formation of one-dimensional structures with an internal 2×3 periodicity, after the deposition of Ba atoms at 970 K or at room temperature followed by a 770 K anneal. Scanning tunneling microscopy (STM) data were compared with theoretically simulated STM images generated by density functional theory electronic structure calculations. Excellent agreement between experiment and simulation was found when using an adopted structural model that assumes partial removal of the surface Ge dimers in the [1–10] surface direction and subsequent addition of a single Ba atom to the substrate second layer. Structural assignments for a number of defects observed within regions of the 2×3 reconstruction were also obtained