Pumping current of a Luttinger liquid with finite length

We study transport properties in a Tomonaga-Luttinger liquid in the presence of two time-dependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I_bs) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of the impurity potentials. We also show how the previous infinite length results for I_bs are modified by the finite size of the system.Comment: 9 pages, 7 figure

One sixth of Amazonian tree diversity is dependent on river floodplains

Amazonia's floodplain system is the largest and most biodiverse on Earth. Although forests are crucial to the ecological integrity of floodplains, our understanding of their species composition and how this may differ from surrounding forest types is still far too limited, particularly as changing inundation regimes begin to reshape floodplain tree communities and the critical ecosystem functions they underpin. Here we address this gap by taking a spatially explicit look at Amazonia-wide patterns of tree-species turnover and ecological specialization of the region's floodplain forests. We show that the majority of Amazonian tree species can inhabit floodplains, and about a sixth of Amazonian tree diversity is ecologically specialized on floodplains. The degree of specialization in floodplain communities is driven by regional flood patterns, with the most compositionally differentiated floodplain forests located centrally within the fluvial network and contingent on the most extraordinary flood magnitudes regionally. Our results provide a spatially explicit view of ecological specialization of floodplain forest communities and expose the need for whole-basin hydrological integrity to protect the Amazon's tree diversity and its function.Naturali