188 research outputs found
Decidability and definability with circumscription
AbstractWe consider McCarthy's notions of predicate circumscription and formula circumscription. We show that the decision problems “does θ have a countably infinite minimal model” and “does φ hold in every countably infinite minimal model of θ” are complete Σ12 and complete π12 over the integers, for both forms of circumscription. The set of structures definable (up to isomorphism) as first order definable subsets of countably infinite minimal models is the set of structures which are Δ12 over the integers, for both forms of circumscription. Thus, restricted to countably infinite structures, predicate and formula circumscription define the same sets and have equally difficult decision problems. With general formula circumscription we can define several infinite cardinals, so the decidability problems are dependent upon the axioms of set theory
Commonsense axiomatizations for logic programs
AbstractVarious semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom
The Expressiveness of Locally Stratified Programs
This paper completes an investigation of the logical expressibility of finite, locally stratified, general logic programs. We show that every hyperarithmetic set can be computed by a suitably chosen locally stratified logic program (as a set of values of a predicate over its perfect model). This is an optimal result, since the perfect model of a locally stratified program is itself an implicitly definable hyperarithmetic set (under a recursive coding of the Herbrand base); hence to obtain all hyperarithmetic sets requires something new, in this case selecting one predicate from the model. We find that the expressive power of programs does not increase when one considers the programs which have a unique stable model or a total well-founded model. This shows that all these classes of structures (perfect models of locally stratified logic programs, well-founded models which turn out to be total, and stable models of programs possessing a unique stable model) are all closely connected with Kleene\u27s hyperarithmetical hierarchy. Thus, for general logic programming, negation with respect to two-valued logic is related to the hyperarithmetic hierarchy in the same way as Horn logic is to the class of recursively enumerable sets
Fluctuation-driven insulator-to-metal transition in an external magnetic field
We consider a model for a metal-insulator transition of correlated electrons
in an external magnetic field. We find a broad region in interaction and
magnetic field where metallic and insulating (fully magnetized) solutions
coexist and the system undergoes a first-order metal-insulator transition. A
global instability of the magnetically saturated solution precedes the local
ones and is caused by collective fluctuations due to poles in electron-hole
vertex functions.Comment: REVTeX 4 pages, 3 PS figure
A closer look into two-step perovskite conversion with X-ray scattering
Recently, hybrid perovskites have gathered much interest as alternative materials for the fabrication of highly efficient and cost-competitive solar cells; however, many questions regarding perovskite crystal formation and deposition methods remain. Here we have applied a two-step protocol where a crystalline PbI2 precursor film is converted to MAPbI3–xClx perovskite upon immersion in a mixed solution of methylammonium iodide and methylammonium chloride. We have investigated both films with grazing incidence small-angle X-ray scattering to probe the inner film morphology. Our results demonstrate a strong link between lateral crystal sizes in the films before and after conversion, which we attribute to laterally confined crystal growth. Additionally, we observe an accumulation of smaller grains within the bulk in contrast with the surface. Thus, our results help to elucidate the crystallization process of perovskite films deposited via a two-step technique that is crucial for controlled film formation, improved reproducibility, and high photovoltaic performance
Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons
A general expansion scheme based on the concept of linked cluster expansion
from the theory of classical spin systems is constructed for models of
interacting electrons. It is shown that with a suitable variational formulation
of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling
the expansion represents a universal and comprehensive tool for systematic
improvements of static mean-field theories. As an example of the general
formalism we investigate in detail an analytically tractable series of ring
diagrams that correctly capture dynamical fluctuations at weak coupling. We
introduce renormalizations of the diagrammatic expansion at various levels and
show how the resultant theories are related to other approximations of similar
origin. We demonstrate that only fully self-consistent approximations produce
global and thermodynamically consistent extensions of static mean field
theories. A fully self-consistent theory for the ring diagrams is reached by
summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file
Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism
We study the Hubbard model with bond-charge interaction (`correlated
hopping') in terms of the Gutzwiller wave function. We show how to express the
Gutzwiller expectation value of the bond-charge interaction in terms of the
correlated momentum-space occupation. This relation is valid in all spatial
dimensions. We find that in infinite dimensions, where the Gutzwiller
approximation becomes exact, the bond-charge interaction lowers the critical
Hubbard interaction for the Brinkman-Rice metal-insulator transition. The
bond-charge interaction also favors ferromagnetic transitions, especially if
the density of states is not symmetric and has a large spectral weight below
the Fermi energy.Comment: 5 pages, 3 figures; minor changes, published versio
The HSE hybrid functional within the FLAPW method and its application to GdN
We present an implementation of the Heyd-Scuseria-Ernzerhof (HSE) hybrid
functional within the full-potential linearized augmented-plane-wave (FLAPW)
method. Pivotal to the HSE functional is the screened electron-electron
interaction, which we separate into the bare Coulomb interaction and the
remainder, a slowly varying function in real space. Both terms give rise to
exchange potentials, which sum up to the screened nonlocal exchange potential
of HSE. We evaluate the former with the help of an auxiliary basis, defined in
such a way that the bare Coulomb matrix becomes sparse. The latter is computed
in reciprocal space, exploiting its fast convergence behavior in reciprocal
space. This approach is general and can be applied to a whole class of screened
hybrid functionals. We obtain excellent agreement of band gaps and lattice
constants for prototypical semiconductors and insulators with
electronic-structure calculations using plane-wave or Gaussian basis sets. We
apply the HSE hybrid functional to examine the ground-state properties of
rocksalt GdN, which have been controversially discussed in literature. Our
results indicate that there is a half-metal to insulator transition occurring
between the theoretically optimized lattice constant at 0 K and the
experimental lattice constant at room temperature. Overall, we attain good
agreement with experimental data for band transitions, magnetic moments, and
the Curie temperature.Comment: 13 pages, 4 figures, 6 table
The Numerical Renormalization Group Method for correlated electrons
The Numerical Renormalization Group method (NRG) has been developed by Wilson
in the 1970's to investigate the Kondo problem. The NRG allows the
non-perturbative calculation of static and dynamic properties for a variety of
impurity models. In addition, this method has been recently generalized to
lattice models within the Dynamical Mean Field Theory. This paper gives a brief
historical overview of the development of the NRG and discusses its application
to the Hubbard model; in particular the results for the Mott metal-insulator
transition at low temperatures.Comment: 14 pages, 7 eps-figures include
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