The weak localization for the alloy-type Anderson model on a cubic lattice

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e. when the coupling parameter $\lambda$ is small, for the energies $E \le -C \lambda^2$.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy

Localization on quantum graphs with random vertex couplings

We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges

Understanding the Random Displacement Model: From Ground-State Properties to Localization

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 201

Lifshitz Tails in Constant Magnetic Fields

We consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained in the case of a vanishing magnetic field

Persistence of Anderson localization in Schr\"odinger operators with decaying random potentials

We show persistence of both Anderson and dynamical localization in Schr\"odinger operators with non-positive (attractive) random decaying potential. We consider an Anderson-type Schr\"odinger operator with a non-positive ergodic random potential, and multiply the random potential by a decaying envelope function. If the envelope function decays slower than $|x|^{-2}$ at infinity, we prove that the operator has infinitely many eigenvalues below zero. For envelopes decaying as $|x|^{-\alpha}$ at infinity, we determine the number of bound states below a given energy $E<0$, asymptotically as $\alpha\downarrow 0$. To show that bound states located at the bottom of the spectrum are related to the phenomenon of Anderson localization in the corresponding ergodic model, we prove: (a) these states are exponentially localized with a localization length that is uniform in the decay exponent $\alpha$; (b)~ dynamical localization holds uniformly in $\alpha$

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.Comment: 29 pages, 1 figure, to appear in AH

Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other

New characterizations of the region of complete localization for random Schr\"odinger operators

We study the region of complete localization in a class of random operators which includes random Schr\"odinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. (These are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region.) Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity

Insights in nutrition programs for the developing ruminant

As the world population grows and resources for food animal production become more limited, animal efficiency must increase. The dairy industry has made progress in reducing age at first calving from 27 to 25 mo., but heifers remain unproductive for over half of their life while still consuming resources. As pre-ruminants, offering restricted amounts of milk to neonatal heifers (conventional system) increases concentrate consumption which drives rumen development. However, accelerated milk programs improve pre-weaning growth rate and the balance between these two systems is still under continuous investigation. Solid feed is important for papillary and musculature development in addition to establishment of a microbial population, which increase transition success when calves are weaned gradually. Furthermore, the optimal target weight for calving is 550 kg at 23 to 24.5 mo., which increases 305-d lactation yield. Increased milk production is desired, but a costly rearing period without producing milk only increases as age at first calving increases, which also increases total number of replacement heifers and total herd green-house emissions. Strategies to achieve desired body weight and age at first calving while reducing input include, using compensatory growth, restricting intake and precision feeding. Compensatory growth can increase average daily gain and feed efficiency; moreover, precision feeding increases feed efficiency even further by reducing nutrient metabolic costs in comparison to ad- libitum systems. Restricting intake provides increased rumen retention time for fiber, non-structural carbohydrates, protein, and other nutrients to be highly digested. Nutrient digestibility is important when comparing these feeding methods because dry matter intake has the greatest impact on efficiency, specifically when different amounts of forages are fed. Using different strategies during the weaning, pre-pubertal and post-pubertal period of dairy heifers can significantly improve performance, nutrient and resources utilization during this conditioning growing phase of dairy cattle.A medida que la población mundial crece y los alimentos se vuelven más limitados, la eficiencia animal debe aumentar. La industria láctea ha progresado en la reducción de la edad al primer parto de 27 a 25 meses, pero las vaquillas siguen siendo improductivas durante más de la mitad de su vida mientras consumen recursos. Como pre-rumiantes, ofrecer cantidades restringidas de leche a las vaquillas neonatales (sistema convencional) aumenta el consumo de concentrado, lo que impulsa el desarrollo del rumen. Sin embargo, los programas acelerados de leche mejoran la tasa de crecimiento previo al destete y el equilibrio entre estos dos sistemas aún está bajo investigación continua. La alimentación sólida es importante para el desarrollo papilar y la musculatura, además del establecimiento de una población microbiana, que aumenta el éxito de la transición cuando los terneros se destetan gradualmente. El peso objetivo para el parto es 550 kg de 23 a 24.5 meses, lo que aumenta el rendimiento de lactancia de 305 días. Si no se reduce el periodo de cría, aumenta el número de vaquillas de reemplazo y las emisiones totales de gases invernadero. Las estrategias para lograr el peso corporal y la edad deseados al primer parto al tiempo que se reducen los insumos incluyen el uso de crecimiento compensatorio, la restricción de la ingesta y la alimentación de precisión. El crecimiento compensatorio puede aumentar la ganancia diaria promedio y la eficiencia alimenticia; Además, la alimentación de precisión aumenta aún más la eficiencia alimenticia al reducir los costos metabólicos de los nutrientes en comparación con los sistemas ad-libitum. La ingesta restringida proporciona un mayor tiempo de retención del rumen para que la fibra, los carbohidratos no estructurales, las proteínas y otros nutrientes sean altamente digeridos