Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology

We construct a categorification of the maximal commutative subalgebra of the type A Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the (non-symmetric) monoidal category of Soergel bimodules. The adjoint of this functor allows one to match the Hochschild homology of any braid with the Euler characteristic of a sheaf on the flag Hilbert scheme. The categorified Jones-Wenzl projectors studied by Abel, Elias and Hogancamp are idempotents in the category of Soergel bimodules, and they correspond to the renormalized Koszul complexes of the torus fixed points on the flag Hilbert scheme. As a consequence, we conjecture that the endomorphism algebras of the categorified projectors correspond to the dg algebras of functions on affine charts of the flag Hilbert schemes. We define a family of differentials dN on these dg algebras and conjecture that their homology matches that of the glN projectors, generalizing earlier conjectures of the first and third authors with Oblomkov and Shende

Learning from a long-term crop rotation experiment

A crop rotation experiment was established in 1996/97 at three locations representing differ-ent soil types and climates. Three factors were tested: i) crop rotation with different propor-tions of N2-fixing crops, ii) with and without a catch crop, and iii) with and without animal manure. A green manure crop increased yields in the following cereal crops, but at the rota-tional level, total yields were larger in crop rotations without a green manure crop. There were positive effects of animal manure and catch crops on yield. However, except for the coarse sandy soil, the yield effects of catch crops and animal manure decreased over time when a grass-clover green manure was included in the rotation. The problems with perennial weeds increased over time depending on crop rotation and use of catch crops. This stresses the im-portance of considering long-term effects in the evaluation of crop management measures

Nitrogen use efficiency of cereals in arable organic farming

The effect of nitrogen (N) supply and weeds on grain yield of spring barley, winter wheat and winter rye was investigated from 1997 to 2004 in an organic farming crop rotation experiment in Denmark on three soil types varying from coarse sand to sandy loam. Two experimental factors were included in the experiment in a factorial design: 1) catch crop (with and without), and 2) manure (with and without). The apparent recovery efficiency of N in grains (nitrogen use efficiency, NUE) from NH4-N in applied manure varied from 29 to 38% in spring barley and from 23 to 44% in winter cereals. The NUE of above-ground N in catch crops sampled in November prior to the spring barley varied from 16 to 52% with the largest value on the coarse sandy soil and the smallest value on the sandy loam soil. The NUE of N accumulated in grass-clover cuttings varied from 14 to 39% with the lowest value on the coarse sandy soil, most likely due to high rates of N leaching. The NUE declined with increasing amounts of N accumulated in the grass-clover cuttings. This indicates that grain yields can be improved by removing the grass-clover cuttings and applying the N contained in the cuttings in spring to the cereal crops, possibly after fermentation in a biogas reactor

Realizing time crystals in discrete quantum few-body systems

The exotic phenomenon of time translation symmetry breaking under periodic driving - the time crystal - has been shown to occur in many-body systems even in clean setups where disorder is absent. In this work, we propose the realization of time-crystals in few-body systems, both in the context of trapped cold atoms with strong interactions and of a circuit of superconducting qubits. We show how these two models can be treated in a fairly similar way by adopting an effective spin chain description, to which we apply a simple driving protocol. We focus on the response of the magnetization in the presence of imperfect pulses and interactions, and show how the results can be interpreted, in the cold atomic case, in the context of experiments with trapped bosons and fermions. Furthermore, we provide a set of realistic parameters for the implementation of the superconducting circuit.Comment: 6 pages, 4 figure

X-Ray Emission from the Warm Hot Intergalactic Medium

The number of detected baryons in the Universe at z<0.5 is much smaller than predicted by standard big bang nucleosynthesis and by the detailed observation of the Lyman alpha forest at red-shift z=2. Hydrodynamical simulations indicate that a large fraction of the baryons today is expected to be in a ``warm-hot'' (10^5-10^7K) filamentary gas, distributed in the intergalactic medium. This gas, if it exists, should be observable only in the soft X-ray and UV bands. Using the predictions of a particular hydrodynamic model, we simulated the expected X-ray flux as a function of energy in the 0.1-2 keV band due to the Warm-Hot Intergalactic Medium (WHIM), and compared it with the flux from local and high red-shift diffuse components. Our results show that as much as 20% of the total diffuse X-ray background (DXB) in the energy range 0.37-0.925keV could be due to X-ray flux from the WHIM, 70% of which comes from filaments at redshift z between 0.1 and 0.6. Simulations done using a FOV of 3', comparable with that of Suzaku and Constellation-X, show that in more than 20% of the observations we expect the WHIM flux to contribute to more than 20% of the DXB. These simulations also show that in about 10% of all the observations a single bright filament in the FOV accounts, alone, for more than 20% of the DXB flux. Red-shifted oxygen lines should be clearly visible in these observations.Comment: 19 pages, 6 figure

Singlet-Triplet Physics and Shell Filling in Carbon Nanotube Double Quantum Dots

An artifcial two-atomic molecule, also called a double quantum dot (DQD), is an ideal system for exploring few electron physics. Spin-entanglement between just two electrons can be explored in such systems where singlet and triplet states are accessible. These two spin-states can be regarded as the two states in a quantum two-state system, a so-called singlet-triplet qubit. A very attractive material for realizing spin based qubits is the carbon nanotube (CNT), because it is expected to have a very long spin coherence time. Here we show the existence of a gate-tunable singlet-triplet qubit in a CNT DQD. We show that the CNT DQD has clear shell structures of both four and eight electrons, with the singlet-triplet qubit present in the four-electron shells. We furthermore observe inelastic cotunneling via the singlet and triplet states, which we use to probe the splitting between singlet and triplet, in good agreement with theory.Comment: Supplement available at: http://www.fys.ku.dk/~hij/public/singlet-triple_supp.pd

Shear Flow Generation and Energetics in Electromagnetic Turbulence

Zonal flows are recognised to play a crucial role for magnetised plasma confinement. The genesis of these flows out of turbulent fluctuations is therefore of significant interest. We investigate the relative importance of zonal flow generation mechanisms via the Reynolds stress, Maxwell stress, and geodesic acoustic mode (GAM) transfer in drift-Alfv\'en turbulence. By means of numerical computations we quantify the energy transfer into zonal flows owing to each of these effects. The importance of the three driving ingredients in electrostatic and electromagnetic turbulence for conditions relevant to the edge of fusion devices is revealed for a broad range of parameters. The Reynolds stress is found to provide a flow drive, while the electromagnetic Maxwell stress is in the cases considered a sink for the flow energy. In the limit of high plasma beta, where electromagnetic effects and Alfv\'en dynamics are important, the Maxwell stress is found to cancel the Reynolds stress to a high degree. The geodesic oscillations, related to equilibrium pressure profile modifications due to poloidally asymmetric transport, can act as both sinks as drive terms, depending on the parameter regime. For high beta cases the GAMs are the main drive of the flow. This is also reflected in the frequency dependence of the flow, showing a distinct peak at the GAM frequency in that regime.Comment: 16 pages, 12 Figure