First-Principles Study on Electron Conduction in Sodium Nanowire

We present detailed first-principles calculations of the electron-conduction properties of a three-sodium-atom nanowire suspended between semi-infinite crystalline Na(001) electrodes during its elongation. Our investigations reveal that the conductance is ~1 G0 before the nanowire breaks and only one channel with the characteristic of the $3s$ orbital of the center atom in the nanowire contributes to the electron conduction. Moreover, the channel fully opens around the Fermi level, and the behavior of the channel-current density is insensitive to the structural deformation of the nanowire. These results verify that the conductance trace as a function of the electrode spacing exhibits a flat plateau at ~1 G0 during elongation.Comment: 8 pages, 5 figure

Emissions Trading and the Polluter-Pays Principle : do Polluters Pay under Grandfathering?

Emissions trading is becoming increasingly popular in environmental law. Allowances to trade emissions can either be auctioned off or handed out free of charge by means of grandfathering. Although grandfathering is frequently used in emissions trading schemes, it is a popular view in the economic and legal literature that grandfathering is inconsistent with the polluter-pays principle. We come to a different, more nuanced view. The question of whether polluters pay under grandfathering depends on how the polluter-pays principle is interpreted. We present a taxonomy of interpretations. Based on an efficiency interpretation of the principle, consistency is demonstrated by emphasizing the economic impact of the opportunity costs of gratis allowances and the lump sum nature of the subsidy that is inherent to grandfathering. Inconsistency can only be claimed based on an equity interpretation of the polluter-pays principle. Allocating allowances free of charge means that polluting firms receive a capital gift making their shareholders richer, which may be perceived as unfair. We draw two conclusions. First, contrary to what some have claimed, grandfathering is compatible with an efficiency interpretation of the polluter-pays principle. Second, only auctioning is consistent with an extended form of this principle. Auctioning ensures not only that pollution costs are internalized (efficiency), but also that producers buy their allowances before they pass on those costs to consumers (equity)