Third quantization: a general method to solve master equations for quadratic open Fermi systems

The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method is applied to the explicit construction of non-equilibrium steady states and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2 chain in a transverse magnetic field.Comment: 24 pages, with 8 eps figures - few minor corrections to the published version, e.g. anti-symmetrizing the matrix given by eq. (27

Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition

We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal driving in terms of the Redfield equation is analyzed in detail. We explain how to compute all physically relevant quantities, such as non-equilibrium expectation values of local observables, various entropies or information measures, or time evolution and properties of relaxation. We also discuss how to exactly treat explicitly time dependent problems. The general formalism is then applied to study a thermally driven open XY spin 1/2 chain. We find that recently proposed non-equilibrium quantum phase transition in the open XY chain survives the thermal driving within the Redfield model. In particular, the phase of long-range magnetic correlations can be characterized by hypersensitivity of the non-equilibrium-steady state to external (bath or bulk) parameters. Studying the heat transport we find negative thermal conductance for sufficiently strong thermal driving, as well as non-monotonic dependence of the heat current on the strength of the bath coupling.Comment: 24 pages, 12 figures, submitted to New Journal of Physics, Focus issue "Quantum Information and Many-Body Theory

Application of unmanned aerial systems for high throughput phenotyping of large wheat breeding nurseries

Citation: Haghighattalab, A., Perez, L. G., Mondal, S., Singh, D., Schinstock, D., Rutkoski, J., . . . Poland, J. (2016). Application of unmanned aerial systems for high throughput phenotyping of large wheat breeding nurseries. Plant Methods, 12, 15. https://doi.org/10.1186/s13007-016-0134-6Background: Low cost unmanned aerial systems (UAS) have great potential for rapid proximal measurements of plants in agriculture. In the context of plant breeding and genetics, current approaches for phenotyping a large number of breeding lines under field conditions require substantial investments in time, cost, and labor. For field-based high-throughput phenotyping (HTP), UAS platforms can provide high-resolution measurements for small plot research, while enabling the rapid assessment of tens-of-thousands of field plots. The objective of this study was to complete a baseline assessment of the utility of UAS in assessment field trials as commonly implemented in wheat breeding programs. We developed a semi-automated image-processing pipeline to extract plot level data from UAS imagery. The image dataset was processed using a photogrammetric pipeline based on image orientation and radiometric calibration to produce orthomosaic images. We also examined the relationships between vegetation indices (VIs) extracted from high spatial resolution multispectral imagery collected with two different UAS systems (eBee Ag carrying MultiSpec 4C camera, and IRIS+ quadcopter carrying modified NIR Canon S100) and ground truth spectral data from hand-held spectroradiometer. Results: We found good correlation between the VIs obtained from UAS platforms and ground-truth measurements and observed high broad-sense heritability for VIs. We determined radiometric calibration methods developed for satellite imagery significantly improved the precision of VIs from the UAS. We observed VIs extracted from calibrated images of Canon S100 had a significantly higher correlation to the spectroradiometer (r = 0.76) than VIs from the MultiSpec 4C camera (r = 0.64). Their correlation to spectroradiometer readings was as high as or higher than repeated measurements with the spectroradiometer per se. Conclusion: The approaches described here for UAS imaging and extraction of proximal sensing data enable collection of HTP measurements on the scale and with the precision needed for powerful selection tools in plant breeding. Low-cost UAS platforms have great potential for use as a selection tool in plant breeding programs. In the scope of tools development, the pipeline developed in this study can be effectively employed for other UAS and also other crops planted in breeding nurseries

Finite thermal conductivity in 1D models having zero Lyapunov exponents

Heat conduction in three types of 1D channels are studied. The channels consist of two parallel walls, right triangles as scattering obstacles, and noninteracting particles. The triangles are placed along the walls in three different ways: (a) periodic, (b) disordered in height, and (c) disordered in position. The Lyapunov exponents in all three models are zero because of the flatness of triangle sides. It is found numerically that the temperature gradient can be formed in all three channels, but the Fourier heat law is observed only in two disordered ones. The results show that there might be no direct connection between chaos (in the sense of positive Lyapunov exponent) and the normal thermal conduction.Comment: 4 PRL page

Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms

The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms underlying the validity of the theoretical predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007

Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations

We study a model of interacting fermions in a disordered potential, which is assumed to generate uniformly fluctuating interaction matrix elements. We show that the ground state magnetization is systematically decreased by off-diagonal fluctuations of the interaction matrix elements. This effect is neglected in the Stoner picture of itinerant ferromagnetism in which the ground-state magnetization is simply determined by the balance between ferromagnetic exchange and kinetic energy, and increasing the interaction strength always favors ferromagnetism. The physical origin of the demagnetizing effect of interaction fluctuations is the larger number of final states available for interaction-induced scattering in the lower spin sectors of the Hilbert space. We analyze the energetic role played by these fluctuations in the limits of small and large interaction $U$. In the small $U$ limit we do second-order perturbation theory and identify explicitly transitions which are allowed for minimal spin and forbidden for higher spin. These transitions then on average lower the energy of the minimal spin ground state with respect to higher spin. For large interactions $U$ we amplify on our earlier work [Ph. Jacquod and A.D. Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is favored due to a larger broadening of the many-body density of states in the low-spin sectors. Numerical results are presented in both limits.Comment: 35 pages, 24 figures - final, shortened version, to appear in Physical Review

Iron bioavailability in two commercial cultivars of wheat: a comparison between wholegrain and white flour and the effects of nicotianamine and 2'-deoxymugineic acid on iron uptake into Caco-2 cells

Iron bioavailability in unleavened white and wholegrain bread made from two commercial wheat varieties was assessed by measuring ferritin production in Caco-2 cells. The breads were subjected to simulated gastrointestinal digestion and the digests applied to the Caco-2 cells. Although Riband grain contained a lower iron concentration than Rialto, iron bioavailability was higher. No iron was taken up by the cells from white bread made from Rialto flour or from wholegrain bread from either variety, but Riband white bread produced a small ferritin response. The results probably relate to differences in phytate content of the breads, although iron in soluble monoferric phytate was demonstrated to be bioavailable in the cell model. Nicotianamine, an iron chelator in plants involved in iron transport, was a more potent enhancer of iron uptake into Caco-2 cells than ascorbic acid or 2'-deoxymugineic acid, another metal chelator present in plants

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change

On the determinants of local government debt: Does one size fit all?

This paper analyzes the factors that directly influence levels of debt in Spanish local governments. Specifically, the main objective is to find out the extent to which indebtedness is originated by controllable factors that public managers can influence, or whether it hinges on other variables beyond managers’ control. The importance of this issue has intensified since the start of the crisis in 2007, due to the abrupt decline of revenues and, simultaneously, to the stagnation (or even increase) in the levels of costs facing these institutions face. Results can be explored from multiple perspectives, given that the set of explanatory factors is also multiple. However, the most interesting result relates to the varying effect of each covariate depending on each municipality’s specific debt level, which suggests that economic policy recommendations should not be homogeneous across local governments