SAT-Inspired Higher-Order Eliminations

We generalize several propositional preprocessing techniques to higher-orderlogic, building on existing first-order generalizations. These techniqueseliminate literals, clauses, or predicate symbols from the problem, with theaim of making it more amenable to automatic proof search. We also introduce anew technique, which we call quasipure literal elimination, that strictlysubsumes pure literal elimination. The new techniques are implemented in theZipperposition theorem prover. Our evaluation shows that they sometimes helpprove problems originating from the TPTP library and Isabelle formalizations.<br

Electronic structure and optical properties of Sn and SnGe quantum dots

Self-assembled quantum dots in a Si–Ge–Sn system attract research attention as possible direct band gap materials, compatible with Si-based technology, with potential applications in optoelectronics. In this work, the electronic structure near the point and interband optical matrix elements of strained Sn and SnGe quantum dots in a Si or Ge matrix are calculated using the eight-band k·p method, and the competing L-valley conduction band states were found by the effective mass method. The strain distribution in the dots was found with the continuum mechanical model. The parameters required for the k·p or effective mass calculation for Sn were extracted by fitting to the energy band structure calculated by the nonlocal empirical pseudopotential method. The calculations show that the self-assembled Sn/Si dots, sized between 4 and 12 nm, have indirect interband transition energies between 0.8 and 0.4 eV and direct interband transitions between 2.5 and 2.0 eV. In particular, the actually grown, approximately cylindrical Sn dots in Si with a diameter and height of about 5 nm are calculated to have an indirect transition (to the L valley) of about 0.7 eV, which agrees very well with experimental results. Similar good agreement with the experiment was also found for SnGe dots grown on Si. However, neither of these is predicted to be direct band gap materials, in contrast to some earlier expectations

Symmetry of k·p Hamiltonian in pyramidal InAs/GaAs quantum dots: Application to the calculation of electronic structure

A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the C-4 symmetry of the 8-band k·p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasiangular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type, and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer's double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands

Extending a Brainiac Prover to Lambda-Free Higher-Order Logic

International audienceDecades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features. We explain how to extend the prover’s data structures, algorithms, and heuristics to $$\lambda$$ λ -free higher-order logic, a formalism that supports partial application and applied variables. Our extension outperforms the traditional encoding and appears promising as a stepping stone toward full higher-order logic

Superposition with First-class {B}ooleans and Inprocessing Clausification

International audienceWe present a complete superposition calculus for first-order logic with an interpreted Boolean type. Our motivation is to lay the foundation for refutationally complete calculi in more expressive logics with Booleans, such as higher-order logic, and to make superposition work efficiently on problems that would be obfuscated when using clausification as preprocessing. Working directly on formulas, our calculus avoids the costly axiomatic encoding of the theory of Booleans into first-order logic and offers various ways to interleave clausification with other derivation steps. We evaluate our calculus using the Zipperposition theorem prover, and observe that, with no tuning of parameters, our approach is on a par with the state-of-the-art approach

Quantum transport in semiconductor quantum dot superlattices: electron-phonon resonances and polaron effects

Electron transport in periodic quantum dot arrays in the presence of interactions with phonons was investigated using the formalism of nonequilibrium Green's functions. The self-consistent Born approximation was used to model the self-energies. Its validity was checked by comparison with the results obtained by direct diagonalization of the Hamiltonian of interacting electrons and longitudinal optical phonons. The nature of charge transport at electron -- phonon resonances was investigated in detail and contributions from scattering and coherent tunnelling to the current were identified. It was found that at larger values of the structure period the main peak in the current -- field characteristics exhibits a doublet structure which was shown to be a transport signature of polaron effects. At smaller values of the period, electron -- phonon resonances cause multiple peaks in the characteristics. A phenomenological model for treatment of nonuniformities of a realistic quantum dot ensemble was also introduced to estimate the influence of nonuniformities on current -- field characteristics

Superposition for Full Higher-order Logic

International audienceWe recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free $\lambda$-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise from the interplay between $\lambda$-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition

Superposition with Lambdas

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of $\lambda$-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning

Effects of rapid thermal annealing on device characteristics of InGaAs/GaAs quantum dot infrared photodetectors

In this work, rapid thermal annealing was performed on InGaAs/GaAs quantum dot infrared photodetectors (QDIPs) at different temperatures. The photoluminescence showed a blueshifted spectrum in comparison with the as-grown sample when the annealing temperature was higher than 700 °C, as a result of thermal interdiffusion of the quantum dots (QDs). Correspondingly, the spectral response from the annealed QDIP exhibited a redshift. At the higher annealing temperature of 800 °C, in addition to the largely redshifted photoresponse peak of 7.4 µm (compared with the 6.1 µm of the as-grown QDIP), a high energy peak at 5.6 µm (220 meV) was also observed, leading to a broad spectrum linewidth of 40%. This is due to the large interdiffusion effect which could greatly vary the composition of the QDs and thus increase the relative optical absorption intensity at higher energy. The other important detector characteristics such as dark current, peak responsivity, and detectivity were also measured. It was found that the overall device performance was not affected by low annealing temperature, however, for high annealing temperature, some degradation in device detectivity (but not responsivity) was observed. This is a consequence of increased dark current due to defect formation and increased ground state energy. © 2006 American Institute of Physic