Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes.

In this paper we investigate the following two questions: Q1: Do there exist optimal proof systems for a given language L? Q2: Do there exist complete problems for a given promise class C? For concrete languages L (such as TAUT or SAT) and concrete promise classes C (such as NP∩coNP, UP, BPP, disjoint NP-pairs etc.), these ques-tions have been intensively studied during the last years, and a number of characterizations have been obtained. Here we provide new character-izations for Q1 and Q2 that apply to almost all promise classes C and languages L, thus creating a unifying framework for the study of these practically relevant questions. While questions Q1 and Q2 are left open by our results, we show that they receive affirmative answers when a small amount on advice is avail-able in the underlying machine model. This continues a recent line of research on proof systems with advice started by Cook and Kraj́ıček [6]

Cubic anisotropy in high homogeneity thin (Ga,Mn)As layers

Historically, comprehensive studies of dilute ferromagnetic semiconductors, e.g., $p$-type (Cd,Mn)Te and (Ga,Mn)As, paved the way for a quantitative theoretical description of effects associated with spin-orbit interactions in solids, such as crystalline magnetic anisotropy. In particular, the theory was successful in explaining {\em uniaxial} magnetic anisotropies associated with biaxial strain and non-random formation of magnetic dimers in epitaxial (Ga,Mn)As layers. However, the situation appears much less settled in the case of the {\em cubic} term: the theory predicts switchings of the easy axis between in-plane $\langle 100\rangle$ and $\langle 110\rangle$ directions as a function of the hole concentration, whereas only the $\langle 100\rangle$ orientation has been found experimentally. Here, we report on the observation of such switchings by magnetization and ferromagnetic resonance studies on a series of high-crystalline quality (Ga,Mn)As films. We describe our findings by the mean-field $p$-$d$ Zener model augmented with three new ingredients. The first one is a scattering broadening of the hole density of states, which reduces significantly the amplitude of the alternating carrier-induced contribution. This opens the way for the two other ingredients, namely the so-far disregarded single-ion magnetic anisotropy and disorder-driven non-uniformities of the carrier density, both favoring the $\langle 100\rangle$ direction of the apparent easy axis. However, according to our results, when the disorder gets reduced a switching to the $\langle 110\rangle$ orientation is possible in a certain temperature and hole concentration range.Comment: 12 pages, 9 figure

Magnetic properties of GaMnAs single layers and GaInMnAs superlattices investigated at low temperature and high magnetic field

Magnetotransport properties of GaMnAs single layers and InGaMnAs/InGaAs superlattice structures were investigated at temperatures from 4 K to 300 K and magnetic fields up to 23 T to study the influence of carriers confinement through different structures. Both single layers and superlattice structures show paramagnetic-to-ferromagnetic phase transition. In GaMnAs/InGaAs superlattice beside the Curie temperature (Tc ~ 40 K), a new phase transition is observed close to 13 K.Comment: 8 pages, 5 figures, Proceedings of the XXXII International School on the Physics of Semiconducting Compounds, Jaszowiec 2003, Polan

Post-growth annealing of GaMnAs under As capping - an alternative way to increase Tc

We demonstrate that in situ post-growth annealing of GaMnAs layers under As capping is adequate for achieving high Curie temperatures (Tc) in a similar way as ex situ annealing in air or in N2 atmosphere practiced earlier.Comment: 13 pages, 4 figure

The deduction theorem for strong propositional proof systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs

Photoemission studies of Ga1−x_{1-x}Mnx_{x}As: Mn-concentration dependent properties

Using angle-resolved photoemission, we have investigated the development of the electronic structure and the Fermi level pinnning in Ga$_{1-x}$Mn$_{x}$As with Mn concentrations in the range 1--6%. We find that the Mn-induced changes in the valence-band spectra depend strongly on the Mn concentration, suggesting that the interaction between the Mn ions is more complex than assumed in earlier studies. The relative position of the Fermi level is also found to be concentration-dependent. In particular we find that for concentrations around 3.5--5% it is located very close to the valence-band maximum, which is in the range where metallic conductivity has been reported in earlier studies. For concentration outside this range, larger as well as smaller, the Fermi level is found to be pinned at about 0.15 eV higher energy.Comment: REVTeX style; 7 pages, 3 figure