Optimal correction of independent and correlated errors

We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant improvements to the fidelity bounds and optimal entanglement decay profiles.Comment: 11 pages, 4 figures. Updated to include fidelity analysi

The traveling salesman problem, conformal invariance, and dense polymers

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.Comment: 4 pages. v2: small revisions, improved argument about dimensions d>2. v3: Final version, with a correction to the form of the tour length in a domain, and a new referenc

Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model

We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely-degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur

Dynamic rotor mode in antiferromagnetic nanoparticles

We present experimental, numerical, and theoretical evidence for a new mode of antiferromagnetic dynamics in nanoparticles. Elastic neutron scattering experiments on 8 nm particles of hematite display a loss of diffraction intensity with temperature, the intensity vanishing around 150 K. However, the signal from inelastic neutron scattering remains above that temperature, indicating a magnetic system in constant motion. In addition, the precession frequency of the inelastic magnetic signal shows an increase above 100 K. Numerical Langevin simulations of spin dynamics reproduce all measured neutron data and reveal that thermally activated spin canting gives rise to a new type of coherent magnetic precession mode. This "rotor" mode can be seen as a high-temperature version of superparamagnetism and is driven by exchange interactions between the two magnetic sublattices. The frequency of the rotor mode behaves in fair agreement with a simple analytical model, based on a high temperature approximation of the generally accepted Hamiltonian of the system. The extracted model parameters, as the magnetic interaction and the axial anisotropy, are in excellent agreement with results from Mossbauer spectroscopy

Organic farming at the farm level - Scenarioes for the future development

The purpose of this report is to present possible impacts of new technology and changes in legislation on the profitability of different types of organic farms. The aim is also to look at both the current and future trends in the organic area in Denmark. Besides the economic aspects, the report also shows the nutrient surplus for selected organic farms. Analyses carried out at the Food and Resource Economic Institute (FOI) have previ-ously shown that price premiums of up to 50% on pig meat and 20% on arable farm products is needed to make the organic production profitable. The price premium on cereals and dairy products have in the 1990’ties been higher than required, but in re-cent years the price premium has dropped, leading to low profitability, especially on arable farms. The organic farms in Denmark consist mainly of two types of farms, full time dairy farms and part time arable farms. The dairy farms constitute 25% of the farms, 50% of the area and they have 80% of the livestock units. The part-time arable farms con-stitute 60% of the farms, 28% of the organic area and they have 5% of the livestock units. Previous predictions made by FOI regarding more part-time farms converting to organic farming have been fulfilled, whereas the conversion to organic pig production has been much lower than expected. Both dairy and arable farms are facing new threats as the organic milk production is still much higher than the consumption, and as the profitability on small arable farms is low. The aim of the project is, therefore, to look at the impact of new technology on the profitability of organic farming. As organic farming in Denmark has experienced leg-islative changes leading to lower use of imported feedstuffs, it was also an aim to look at the impact of legislative changes, allowing only 100% organic feed, straw and ma-nure. To analyse this eight case farms were selected as typical organic farms. They con-sisted of 3 dairy farms, 4 arable farms and 1 pig farm. The area and the production on these case farms were based on interviews with local consultants, but they are not ac-tual farms found in Denmark. The intension was to present the typical future organic farm in terms of size, area and crop rotation. The yields and the machinery on these farms were determined in close co-operation with researchers at Danish Institute of Agricultural Sciences (Bygholm). The analyses regarding the profit shows on case farms a profit on the dairy and pig farms and a negative result on the arable case farms. This is comparable with net prof-its found nationally on organic farms in 2002. The capital invested in machinery on case farms is lower than found on actual organic farms due to the optimization proce-dure used to find the right level of machinery. The analyses also show that there does not seem to be significant differences in the machinery costs between conventional and organic farms. The analysis is based on 16 organic and 14 conventional study farms, which makes costs comparable. The ma-chinery costs on the case farms are in line with machinery costs on organic study farms, where most farms have costs between 3,000 and 7,000 DKK per ha (100 DKK = 13.4 €). The impact of new technology is analysed, focusing on the technologies which are found to be available in the near future and where the first trials look promising. The technologies analysed include robotic weeding, band streaming before sowing, use of GPS when applying animal manure and automatic milking using a robot. Both weed management technologies are found to be profitable and to be recommended for fur-ther development. The purpose is to remove weeds inside the row. GPS might give some economic benefits, but will be more profitable in a scenario with restrictions on nitrogen use. More trials have to be conducted to determine whether GPS is profit-able. Automatic milking is not a technology exclusive to the organic sector. The analyses show that if the capacity is well used it might be profitable. As a whole, the technologies do not seem to have a major impact on the future development in the or-ganic sector as the focus is on relatively specialised crops which cover a small area. For the technologies which can be used more widely, the improvement in income is limited. The difference between organic production and conventional farming has diminished over recent years as conventional farmers use less pesticide and mineral fertiliser. Furthermore, the European rules for organic farming might change. The possible im-pact of changes in legislation has, therefore, been analysed. The changes include the following restrictions: • 100% organic feed (requirement from 2005 on dairy farms) • 100% organic straw (no import of conventional straw) • 100% organic manure (no import of conventional manure) 100% organic feed has already been introduced for dairy farms in Denmark, whereas for pig farms it will increase feed costs by 10-17%, but the production will still be profitable. Using 100% organic straw will increase income on arable farms a little and lower the income on livestock farms with few cereal crop areas. The 100% organic manure scenario will reduce the manure (slurry and farm yard ma-nure) used in the organic sector by approximately 20% and increase the price from 5 to approximately 10 DKK per kg N. The effect is a decrease in application of 10 kg effective N per ha. The analyses show that dairy farms will increase their export and apply less than today, whereas arable farms will only reduce their N application a lit-tle. The loss in income among the arable farms is, in the calculation, almost the same as the gains made by the dairy farms, as the yield reductions are limited. However, in the analyses, it is expected that arable farms already today pay for manure imports, which is often not the case. This implies that the costs for organic arable farms found in this analysis under estimate the actual costs. This will also make it more difficult for con-ventional farms to export their manure. Another assumption is that transportation costs are minimal. However, this legislation will imply transportation of manure from livestock intensive areas to arable areas. The total cost of this is roughly estimated at 10-13 million DKK or 700-1,000 DKK per ha for the arable farms in Zealand which receive the manure. Alternatively, the arable farms would have to either have their own livestock or farm without the use of animal manure. The conclusion is that such a legislation will reduce the income on arable farms and increase the income on dairy farms and that it would lead to a change in the regional distribution of farms as livestock and arable farms would have to be located close to each other to reduce transportation costs. For dairy and arable farms located close to each other, such legislation would not necessarily lead to much lower profit for the farms seen as a whole as the animal manure might be utilised bet-ter. Whether the prices for agricultural products could increase in case where they are 100% organic, is questionable and is, therefore, not included in the calculation. In the last chapter, the nutrient balance is estimated on the case farms in the baseline and with a 100% organic manure scenario. The nutrient balance in the baseline shows a nitrogen surplus of 47-110 kg N per ha. The most difficult input to estimate is the N-fixation, which varies with yield and application of animal manure. The case farms have a phosphorus (P) surplus of around zero. For potassium (K) some farms have a surplus others a deficit of up to 90 kg K per ha. In the 100% organic manure scenario, the lower manure application affects the sur-plus more than the slightly lower yields, leading to lower N-surplus, P deficit and lar-ger K deficit than in the baseline scenario. It should be noted that attempts in terms of applying other P and K sources have not been included. The final chapter deals with conclusions and perspectives on the future of organic farming at the farm level. For the dairy farms, there needs to be a better balance be-tween production and demand. This will probably lead to a reduction in the amount of milk which is given the price premium by 30-40%. In the case where these farms stop as organic farms they will reduce the organic area by 30,000 ha. The organic area could therefore be reduced to 130,000 ha. With the lower organic area it is not likely that the organic milk production will exceed 10% of the total Danish milk production. However, it is also likely that farms which stop organic production will continue with an environmentally friendly production not using pesticides and with a limit on the nitrogen application. Many organic farmers have, over the years, come to appreciate this type of production. So although some might change back to conventional farm-ing, they will still use less pesticides than conventional farmers and use the crop rota-tion more actively in order to reduce N-leaching. A smaller organic dairy sector will make the 100% organic manure scenario more costly as the amount of organic ma-nure is lower. The small part time arable farms will probably carry on as the main income comes from outside farming. The challenge is to make efficient large arable farms profitable and in order to do so, they will have to be very large and be efficient. The trend will probably continue away from a subsidy for organic production and to-wards a subsidy for the environmental benefits. The current subsidy level in Denmark is not likely to be increased and the price premium seems to be declining. This indi-cates that the organic as well as the conventional farms will have to be more efficient to be profitable

Quasiclassical theory for the superconducting proximity effect in Dirac materials

We derive the quasiclassical non-equilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati-parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wavefunction inside the F. Fields parallel to the transport direction lead to phase-shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S-junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias, and determine the dependence on the length of the N and F regions and the exchange field.Comment: 13 pages, 5 figures. Accepted for publication in Phys. Rev.

Critical Temperature and Tunneling Spectroscopy of Superconductor-Ferromagnet Hybrids with Intrinsic Rashba-Dresselhaus Spin-Orbit Coupling

We investigate theoretically how the proximity effect in superconductor/ferromagnet hybrid structures with intrinsic spin-orbit coupling manifests in the density of states and critical temperature. To describe a general scenario, we allow for both Rashba and Dresselhaus type spin-orbit coupling. Our results are obtained via the quasiclassical theory of superconductivity, extended to include spin-orbit coupling in the Usadel equation and Kupriyanov--Lukichev boundary conditions. Unlike previous works, we have derived a Riccati parametrization of the Usadel equation with spin-orbit coupling which allows us to address the full proximity regime. First, we consider the density of states in both SF bilayers and SFS trilayers, where the spectroscopic features in the latter case are sensitive to the phase difference between the two superconductors. We find that the presence of spin-orbit coupling leaves clear spectroscopic fingerprints in the density of states due to its role in creating spin-triplet Cooper pairs. Unlike SF and SFS structures without spin-orbit coupling, the density of states in the present case depends strongly on the direction of magnetization. We show that the spin-orbit coupling can stabilize singlet superconductivity even in the presence of a strong exchange field $h \gg \Delta$. This leads to the possibility of a magnetically tunable minigap: changing the direction of the exchange field opens and closes the minigap. We also determine how the critical temperature $T_c$ of an SF bilayer is affected by spin-orbit coupling and demonstrate that one can achieve a spin-valve effect with a single ferromagnet. We find that $T_c$ displays highly non-monotonic behavior both as a function of the magnetization direction and the type and direction of the spin-orbit coupling, offering a new way to exert control over the superconductivity of proximity structures.Comment: 25 pages, 21 figures. Accepted for publication in Phys. Rev.