Exponential Decay of Correlations Implies Area Law

We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: It shows that unless a pure state quantum computation involves states with long-range correlations, decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory - including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem - and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.Comment: 35 pages, 6 figures; v2 minor corrections; v3 published versio

Long-term application of compost versus other organic fertilizers: effects on phosphorus leaching

Many agricultural soils in north-west Europe contain an amount of phosphorus that not only exceeds the crop's needs, but is also an important source of diffusive P losses to the environment. The restriction of P fertilization also implies a restricted application of organic fertilizers and soil improvers as sources of carbon. Our objective was to compare organic fertilizers in their ability to increase the soil organic carbon level, and their influence on P leaching. Three long-term field trials were conducted where fertilization with compost, farmyard manure, digestates, cattle slurry and mineral fertilizers was compared, to determine soil P availability, soil organic carbon level and the soil P content. Soil samples of the tillage layer (0-30 cm) were used in a leaching experiment in controlled unsaturated conditions. This experiment revealed differences in susceptibility to P leaching between the fertilizer types. We observed that compost based on green waste materials is a better option than cattle farmyard manure to increase the soil organic carbon level, without further increasing P losses in soils with highly elevated P levels. Although farmyard manure has a potential to increase the soil organic carbon level comparable to that of compost, the use of farmyard manure stimulates increased soil P availability and P leaching. The solid fraction of mechanically separated digestate also stimulated increases in soil P availability and P leaching. Stopping P fertilization had an immediate decreasing effect on soil P availability. However, continued zero P fertilization over 4 years did not further decrease soil P availability

Типы переводческих ошибок в системе речепорождения

This study was set up to identify the role of dairy farmyard manure and green waste or farm compost used as a source of stable organic matter on soil P availability and P leaching. We sampled two long term field trials (8 and 16 years) on silt loam soil, with continuous amendment of dairy farmyard manure (FYM) and 6 types of organic waste (VFG, BIO), municipal solid waste (MSW), sludge (GWS) or organic farm waste (CMC1, CMC2) composts. Soil P availability was measured as 0.01 M CaCl2 extractable P (P-CaCl2) and hot water extractable P (HWP) and fresh subsamples were used to conduct a leaching experiment in unsaturated conditions in the laboratory. Since the P fertilization history was not equal among the treatments, P leaching concentrations (TP) were standardized with the total P content of the soil (Ptot). P-CaCl2, HWP and the P leaching experiment revealed that in long term farmyard manure amended soils, more P becomes available and is susceptible to leaching than in long term VFG, BIO, MSW, CMC1 and CMC2 compost amended soils. We observed a seasonal trend in P-CaCl2 with minimum and maximum at end of winter (February) and mid-summer (July), respectively. Although this trend was independent of the fertilizer type amended on the soil, the P-CaCl2 significantly increased for farmyard manure amended soil, compared to compost amended soil at any time during the sampling period of >1 year. A sorption experiment with radiolabelled orthophosphoric acid (33PO4) revealed that increased soil P availability and P leaching are related to a decrease in orthophosphate sorption in farmyard manure amended soils, which was not observed in compost amended soils. It is concluded that farmyard manure derived P is more available and more prone to leaching compared to compost derived P due to differences in PO4 sorption

Soil erosion rates under different tillage practices in central Belgium : new perspectives from a combined approach of rainfall simulations and ⁷Be measurements

Recent European Common Agricultural Policy (CAP) forces Flemish farmers in the Belgian loess belt to combat soil erosion on high erosion sensitive parcels. A possible measure against erosion is the application of reduced tillage operations. To evaluate the efficiency of reduced tillage practices, erosion rates of a maize field under conventional tillage, non-inversion tillage and strip-till were compared, all with and without wheel track compaction. To assess erosion rates, 20 min rainfall simulations in combination with fallout radionuclide (FRN) Be-7 measurements were used. At the small plot scale (5 m(2)), runoff coefficient, suspended sediment concentration and soil loss were measured directly during rainfall simulation in order to compare the effect of the different tillage treatments and the effect of wheel track compaction. After the rainfall simulations soil samples were taken for Be-7 analysis to explore spatial patterns in soil redistribution within the different plots. Furthermore, a total soil redistribution budget was obtained based on the Be-7 measurements and validated with the direct erosion measurements during the rainfall simulations. Direct measurements showed a significant decrease in runoff coefficient, suspended sediment concentration and total soil loss in the non-inversion and strip-till treatments compared to the conventional tillage treatment. No difference was observed between the non-inversion and strip-till treatment. For all treatments, wheel track compaction increased runoff coefficients and soil loss. The Be-7 measurements confirmed overall trends observed during the rainfall simulations, with high soil losses in the conventional treatment (5.96 +/- 1.37 kg-6.23 +/- 2.36 kg) and a decrease in soil loss with the non-inversion (1.50 +/- 0.34 kg-1.95 +/- 0.54 kg) and the strip-till treatment (-0.19 +/- 0.60 kg-0.10 +/- 2.50 kg). However, Be-7-derived net erosion estimates overestimated total soil loss per plot compared to the direct measurements. The appropriateness of correction factors, like particle size correction and variations in relaxation mass depth, to improve the tracer based assessment of absolute soil loss values was evaluated. Spatial patterns in soil redistribution clearly reflected the sediment and runoff buffering capacity of the inter-row area in the strip till treatment, while higher erosion rates were observed in the plant rows. Yet, sample representativeness to construct the soil erosion budget is a key consideration in light of discrepancies between tracer and rainfall simulation results. The different rainfall simulations support the preference of non-inversion tillage and strip-till over conventional tillage in order to reduce soil loss in the Belgian loess belt. The increased soil loss due to wheel track compaction implies the need to till favorable soil moisture conditions to avoid soil compaction

Fertilizer value and nitrogen transfer efficiencies with clover-grass ley biomass based fertilizers

In temperate regions, legume-based green manures are a key element of organic rotations. However, specialized farms lack sufficient mobile organic fertilizers. To gain a better understanding of the N flows and the nitrogen (N) and phosphorus (P) fertilizer value of different clover-grass-based fertilizers (biogas digestate, compost, silage and fresh clover-grass obtained from clover grass ley biomass), we assessed their fertilizer value. Nitrogen and P offtake by the ryegrass was used to assess the shortterm effects. The data were completed using model calculations to assess the field-to-field N-transfer efficiencies and the overall N-transfer efficiencies. The greatest plant N offtake was achieved with digestates (64%) and the lowest from the compost (6%) and solid farmyard manure (14%). The mineralization rate was positively related to the NH4+– N/total N ratio (P\0.01, r2 = 0.82). The model calculations indicate that the overall short-term N-transfer efficiencies are driven by the field to-field N-transfer efficiency and the field-to-crop transfer efficiency. However, in the long term, model calculations indicate that a high field-to-field N-transfer efficiency is the key strategic approach when aiming to achieve cropping systems with a high overall longterm N-transfer efficiency. Consequently, the results showed that aerobic decomposition (composting) significantly lowered field-to-field as well as field-tocrop N-transfer rates. The relative P use efficiency strongly differed among the fertilizers. In particular, freshly cut clover-grass and solid manure increased P availability and led to an increase of plant P offtake that was higher than the amount of P supplied