Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develop a computational efficient way to calculate the ES of low-excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation structure. The low-lying shell are robust and survive even for strong electron-electron interactions.Comment: 6 pages 4 figure

Ulta-slow relaxation in discontinuous-film based electron glasses

We present field effect measurements on discontinuous 2D thin films which are composed of a sub monolayer of nano-grains of Au, Ni, Ag or Al. Like other electron glasses these systems exhibit slow conductance relaxation and memory effects. However, unlike other systems, the discontinuous films exhibit a dramatic slowing down of the dynamics below a characteristic temperature $T^*$. $T^*$ is typically between 10-50K and is sample dependent. For $T<T^*$ the sample exhibits a few other peculiar features such as repeatable conductance fluctuations in millimeter size samples. We suggest that the enhanced system sluggishness is related to the current carrying network becoming very dilute in discontinuous films so that the system contains many parts which are electrically very weakly connected and the transport is dominated by very few weak links. This enables studying the glassy properties of the sample as it transitions from a macroscopic sample to a mesocopic sample, hence, the results provide new insight on the underlying physics of electron glasses.Comment: 4 pages, 4 figure

The effect of steepness of temporal resource gradients on spatial root allocation

Plants are able to discriminately allocate greater biomass to organs that grow under higher resource levels. Recent evidence demonstrates that split-root plants also discriminately allocate more resources to roots that grow under dynamically improving nutrient levels, even when their other roots grow in richer patches. Here, we further tested whether, besides their responsiveness to the direction of resource gradients, plants are also sensitive to the steepness of environmental trajectories. Split-root Pisum sativum plants were grown so that one of their roots developed under constantly-high nutrient levels and the other root was subjected to dynamically improving nutrient levels of variable steepness. As expected, plants usually allocated a greater proportion of their biomass to roots that developed under constantly high resource availability; however, when given a choice, they allocated greater biomass to roots that initially experienced relatively low but steeply improving nutrient availabilities than to roots that developed under continuously-high nutrient availability. Such discrimination was not observed when the roots in the poor patch experienced only gentler improvements in nutrient availability. The results are compatible with the notion that responsiveness to the direction and steepness of environmental gradients could assist annual plants to increase their performance by anticipating resource availabilities foreseeable before the end of the growing season. The results exemplify the ability of plants to integrate and utilize environmental information and execute adaptive behaviors which, until recently, were attributed only to animals with central nervous systems