Which canonical algebras are derived equivalent to incidence algebras of posets?

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras whose number of weights is either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr

Module Varieties over Canonical Algebras

AbstractThe main purpose of this paper is the study of module varieties over the class of canonical algebras, providing a rich source of examples of varieties with interesting properties. Our main tool is a stratification of module varieties, which was recently introduced by Richmond. This stratification does not require a precise knowledge of the module category. If it is finite, then it provides a method to classify irreducible components. We determine the canonical algebras for which this stratification is finite. In this case, we describe the algorithm for calculating the dimension of the variety and the number of irreducible components of maximal dimension. For an infinite family of examples we give easy combinatorial criteria for irreducibility, Cohen–Macaulay and normality

Kondo effect in a one-electron double quantum dot: Oscillations of the Kondo current in a weak magnetic field

We present transport measurements of the Kondo effect in a double quantum dot charged with only one or two electrons, respectively. For the one electron case we observe a surprising quasi-periodic oscillation of the Kondo conductance as a function of a small perpendicular magnetic field |B| \lesssim 50mT. We discuss possible explanations of this effect and interpret it by means of a fine tuning of the energy mismatch of the single dot levels of the two quantum dots. The observed degree of control implies important consequences for applications in quantum information processing

Telegraph Noise in Coupled Quantum Dot Circuits Induced by a Quantum Point Contact

Charge detection utilizing a highly biased quantum point contact has become the most effective probe for studying few electron quantum dot circuits. Measurements on double and triple quantum dot circuits is performed to clarify a back action role of charge sensing on the confined electrons. The quantum point contact triggers inelastic transitions, which occur quite generally. Under specific device and measurement conditions these transitions manifest themselves as bounded regimes of telegraph noise within a stability diagram. A nonequilibrium transition from artificial atomic to molecular behavior is identified. Consequences for quantum information applications are discussed.Comment: 4 pages, 3 figures (as published

The structure of fluid trifluoromethane and methylfluoride

We present hard X-ray and neutron diffraction measurements on the polar fluorocarbons HCF3 and H3CF under supercritical conditions and for a range of molecular densities spanning about a factor of ten. The Levesque-Weiss-Reatto inversion scheme has been used to deduce the site-site potentials underlying the measured partial pair distribution functions. The orientational correlations between adjacent fluorocarbon molecules -- which are characterized by quite large dipole moments but no tendency to form hydrogen bonds -- are small compared to a highly polar system like fluid hydrogen chloride. In fact, the orientational correlations in HCF3 and H3CF are found to be nearly as small as those of fluid CF4, a fluorocarbon with no dipole moment.Comment: 11 pages, 9 figure

Non-liftable Calabi-Yau spaces

We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and D. van Straten.Comment: 16 pages, 5 tables; v2: minor corrections and addition

All-electron GW calculation based on the LAPW method: application to wurtzite ZnO

We present a new, all-electron implementation of the GW approximation and apply it to wurtzite ZnO. Eigenfunctions computed in the local-density approximation (LDA) by the full-potential linearized augmented-plane-wave (LAPW) or the linearized muffin-tin-orbital (LMTO) method supply the input for generating the Green function G and the screened Coulomb interaction W. A mixed basis is used for the expansion of W, consisting of plane waves in the interstitial region and augmented-wavefunction products in the augmentation-sphere regions. The frequency-dependence of the dielectric function is computed within the random-phase approximation (RPA), without a plasmon-pole approximation. The Zn 3d orbitals are treated as valence states within the LDA; both core and valence states are included in the self-energy calculation. The calculated bandgap is smaller than experiment by about 1eV, in contrast to previously reported GW results. Self-energy corrections are orbital-dependent, and push down the deep O 2s and Zn 3d levels by about 1eV relative to the LDA. The d level shifts closer to experiment but the size of shift is underestimated, suggesting that the RPA overscreens localized states.Comment: 10 pages, 3 figures, submitted to Phys. Rev.

Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic

Anomalous relaxations and chemical trends at III-V nitride non-polar surfaces

Relaxations at nonpolar surfaces of III-V compounds result from a competition between dehybridization and charge transfer. First principles calculations for the (110) and (10$\bar{1}$0) faces of zincblende and wurtzite AlN, GaN and InN reveal an anomalous behavior as compared with ordinary III-V semiconductors. Additional calculations for GaAs and ZnO suggest close analogies with the latter. We interpret our results in terms of the larger ionicity (charge asymmetry) and bonding strength (cohesive energy) in the nitrides with respect to other III-V compounds, both essentially due to the strong valence potential and absence of $p$ core states in the lighter anion. The same interpretation applies to Zn II-VI compounds.Comment: RevTeX 7 pages, 8 figures included; also available at http://kalix.dsf.unica.it/preprints/; improved after revie