Persistent Currents in Multichannel Interacting Systems

Persistent currents of disordered multichannel mesoscopic rings of spinless interacting fermions threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock methods. The validity of the Hartree-Fock approximation is controled by a direct comparison with the exact results on small $4\times4$ clusters. For sufficiently large disorder (diffusive regime), the effect of repulsive interactions on the current distribution is to slightly decrease its width (mean square current) but to {\it increase} its mean value (mean current). This effect is stronger in the case of a long range repulsion. Our results suggest that the coupling between the chains is essential to understand the large currents observed experimentally.Comment: Revised version, uuencoded compressed file including fig

Quantifying crop pollinator-dependence and pollination deficits: the effects of experimental scale on yield and quality assessments

Many crops are known to be dependent on biotic pollination, but knowledge gaps remain regarding the extent of this dependence, how it varies between crop varieties, and the implications of biotic pollination for crop quality. Data is also lacking on the prevalence and extent of pollination deficits and the ability of the surrounding pollinator community to provide pollination services. Robust and standardised methodologies are crucial for pollination studies. However, there has been only limited research into the critical question of the appropriate scale to apply these methods. Here, we use a commercially important UK apple Malus domestica variety (Gala) to address the questions of pollinator-dependence and pollination deficits, quality benefits arising from pollination, and the implications of conducting pollination experiments at three different scales: the inflorescence, the branch, and the whole plant. We found that Gala apple production was highly dependent on biotic pollination: overall, pollinator exclusion reduced fruit set at harvest to 55% of open pollination levels, whilst supplementary pollination led to fruit set of 167%. However, significant differences were found between the inflorescence, branch, and tree experiments; with increasing scale of observation leading to a lower measure of pollinator-dependence and pollination deficit. At the inflorescence scale, fruit set at harvest was just 13% of normal levels following pollinator exclusion, whilst at the branch and tree scales it was 75% and 79% of normal levels respectively. Supplementary pollination led to fruit set of 218%, 172%, and 117% of normal rates at the inflorescence, branch, and tree scales respectively. Apple seed set was also significantly affected by pollination treatment and the extent of this effect also depended on experimental scale. These differences due to experimental scale are likely a combination of methodological, biological and crop management factors. Seed numbers were shown to be a very good indicator of a number of fruit quality parameters, with greater seed numbers resulting in greater production of Class 1 (i.e. top commercial value) fruit. It is recommended that to measure pollinator-dependence and pollination deficits, experiments are conducted at the largest scale practicable and that treatment effects are monitored until harvest to more accurately reflect final yield outcomes. For apples, growers are recommended to record seed number as part of their fruit quality monitoring programmes to give a rapid and easy to measure indication of potential pollination deficit