Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large or bulk systems. Functionals whose energy is convex for fractional charges such as LDA display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an important paradox and opens the possibility to obtain accurate band-gaps from DFT.Comment: 4 pages 4 figure

The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified for states with both fractional charge and fractional spin: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. This sheds light on the nature of the derivative discontinuity and calls for explicitly discontinuous functionals of the density or orbitals that go beyond currently used smooth approximations. This is key for the application of DFT to strongly correlated systems.Comment: 5 pages 2 figure

Fermionic statistics in the strongly correlated limit of Density Functional Theory

Exact pieces of information on the adiabatic connection integrand $W_{\lambda}[\rho]$, which allows to evaluate the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit ($\lambda\to\infty$, where $\lambda$ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the fermionic statistics at large coupling $\lambda$, both numerical and theoretical, confirming that spin effects enter at orders $\sim e^{-\sqrt{\lambda}}$

Type-II Bose-Mott insulators

The Mott insulating state formed from bosons is ubiquitous in solid He-4, cold atom systems, Josephson junction networks and perhaps underdoped high-Tc superconductors. We predict that close to the quantum phase transition to the superconducting state the Mott insulator is not at all as featureless as is commonly believed. In three dimensions there is a phase transition to a low temperature state where, under influence of an external current, a superconducting state consisting of a regular array of 'wires' that each carry a quantized flux of supercurrent is realized. This prediction of the "type-II Mott insulator" follows from a field theoretical weak-strong duality, showing that this 'current lattice' is the dual of the famous Abrikosov lattice of magnetic fluxes in normal superconductors. We argue that this can be exploited to investigate experimentally whether preformed Cooper pairs exist in high-Tc superconductors.Comment: RevTeX, 17 pages, 6 figures, published versio

Spectra of weighted algebras of holomorphic functions

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach-Stone type question is addressed.Comment: 25 pages Corrected typo

A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability). These axioms are explicitly verified in the case of free fields of various spins, as well as 1+1 conformal field theories. The validity of the axioms for other interacting theories is discussed.Comment: 44 pages, 1 fig. v3: clarified Sec. 2; signs, factors/notation corrected in Eq. 75-80, 105-107; reflects published version. v4: clearer axioms in Sec. 2.3, fixed compensating factor of 2 errors in Eq. 54,74 etc., and other errors. Results unaffected. v5: fixed typos. v6: replaced faulty 1+1 CFT argument, added note on recent progres

Stable Water Isotopes Reveal Effects of Intermediate Disturbance and Canopy Structure on Forest Water Cycling

Forests play an integral role in the terrestrial water cycle and link exchanges of water between the land surface and the atmosphere. To examine the effects of an intermediate disturbance on forest water cycling, we compared vertical profiles of stable water vapor isotopes in two closely located forest sites in northern lower Michigan. At one site, all canopy‐dominant early successional species were stem girdled to induce mortality and accelerate senescence. At both sites, we measured the isotopic composition of atmospheric water vapor at six heights during three seasons (spring, summer, and fall) and paired vertical isotope profiles with local meteorology and sap flux. Disturbance had a substantial impact on local water cycling. The undisturbed canopy was moister, retained more transpired vapor, and at times was poorly mixed with the free atmosphere above the canopy. Differences between the disturbed and undisturbed sites were most pronounced in the summer when transpiration was high. Differences in forest structure at the two sites also led to more isotopically stratified vapor within the undisturbed canopy. Our findings suggest that intermediate disturbance may increase mixing between the surface layer and above‐canopy atmosphere and alter ecosystem‐atmosphere gas exchange.Plain Language SummaryForests play an important role in the climate system and link water fluxes between the land surface and the atmosphere. Here we compare water vapor isotopes in two adjacent forest sites in the northern lower peninsula of Michigan to understand the effects of intermediate disturbance and canopy structure on forest water cycling. One site is dominated by aspen and birch and has a thick, closed canopy. All of the aspen and birch were killed at the second site. As a result, the disturbed site has a more open‐canopy structure. From our comparison, we found that both the species of tree and the spacing around trees are important controls on forest water cycling. With more space between trees, air mixes more freely into the canopy, which dries the forest air. Alternatively, air may be poorly mixed within and above thick, closed canopies.Key PointsIntermediate disturbance can change the contribution of entrained, evaporated, and transpired water vapor to forest canopiesCanopy gaps increase hydrologic mixing between the surface layer and the free atmosphereThe assumption of a well‐mixed canopy atmosphere may be violated in the case of thick, homogeneous forest canopiesPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152563/1/jgrg21482_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152563/2/jgrg21482.pd

An isotopic approach to partition evapotranspiration in a mixed deciduous forest

Transpiration (T) is perhaps the largest fluxes of water from the land surface to the atmosphere and is susceptible to changes in climate, land use and vegetation structure. However, predictions of future transpiration fluxes vary widely and are poorly constrained. Stable water isotopes can help expand our understanding of land–atmosphere water fluxes but are limited by a lack of observations and a poor understanding of how the isotopic composition of transpired vapour (δT) varies. Here, we present isotopic data of water vapour, terrestrial water and plant water from a deciduous forest to understand how vegetation affects water budgets and land–atmosphere water fluxes. We measured subdiurnal variations of δ18OT from three tree species and used water isotopes to partition T from evapotranspiration (ET) to quantify the role of vegetation in the local water cycle. We find that δ18OT deviated from isotopic steady‐state during the day but find no species‐specific patterns. The ratio of T to ET varied from 53% to 61% and was generally invariant during the day, indicating that diurnal evaporation and transpiration fluxes respond to similar atmospheric and micrometeorological conditions at this site. Finally, we compared the isotope‐inferred ratio of T to ET with results from another ET partitioning approach that uses eddy covariance and sap flux data. We find broad midday agreement between these two partitioning techniques, in particular, the absence of a diurnal cycle, which should encourage future ecohydrological isotope studies. Isotope‐inferred estimates of transpiration can inform land surface models and improve our understanding of land–atmosphere water fluxes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/162787/2/eco2229.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162787/1/eco2229_am.pd

Governance of Offshore IT Outsourcing at Shell Global Functions IT-BAM Development and Application of a Governance Framework to Improve Outsourcing Relationships

The lack of effective IT governance is widely recognized as a key inhibitor to successful global IT outsourcing relationships. In this study we present the development and application of a governance framework to improve outsourcing relationships. The approach used to developing an IT governance framework includes a meta model and a customization process to fit the framework to the target organization. The IT governance framework consists of four different elements (1) organisational structures, (2) joint processes between in- and outsourcer, (3) responsibilities that link roles to processes and (4) a diverse set of control indicators to measure the success of the relationship. The IT governance framework is put in practice in Shell GFIT BAM, a part of Shell that concluded to have a lack of management control over at least one of their outsourcing relationships. In a workshop the governance framework was used to perform a gap analysis between the current and desired governance. Several gaps were identified in the way roles and responsibilities are assigned and joint processes are set-up. Moreover, this workshop also showed the usefulness and usability of the IT governance framework in structuring, providing input and managing stakeholders in the discussions around IT governance