Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

The Development of a Process-Structure-Properties-Performance (PSPP) Map for Aluminum-Zinc-Magnesium-Copper Alloys Used in Aircraft Applications

Presented at the 23rd IFHTSE (International Federation for Heat Treatment and Surface Engineering) Congress, Savannah, GA, April 18-22, 2016.In 2011, the White House announced the Materials Genome Initiative, which aims to cut down the cost and time required to discover, develop, and optimize a material and deploy it in a commercial system. One method of achieving this is by integrating experimental test methods, computational tools, and known knowledge databases. While the potential for computational models to speed and assist process-structure-property optimization is not a new concept, one of the key issues in the implementation of models in this space is the lack of a standard method of communication regarding the physical and chemical mechanisms that drive a materials system, and the amount and type of data required to accurately characterize that materials system in its entirety. This work focuses on developing process-structure-property-performance (PSPP) maps as this missing standard communication method. Here we detail the steps that should be taken to generate a map for any system, and then briefly discuss how those steps were applied to high-strength Al-Zn-Mg- Cu alloys. These alloys are highly utilized in aircraft applications and are extremely complicated and commercially viable materials which are repeatedly subject to re-optimization, and are thus a good example of the value of these maps and how they can be used

Robust magnetometry with single nitrogen-vacancy centers via two-step optimization

Shallow nitrogen-vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization and readout process. In a second step, we optimize microwave pulses for pulsed optically detected magnetic resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below 1μT Hz-12 for an 83% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100 nT Hz-12 giving a twofold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications

Introduction to quantum optimal control for quantum sensing with nitrogen-vacancy centers in diamond

Diamond based quantum technology is a fast emerging field with both scientific and technological importance. With the growing knowledge and experience concerning diamond based quantum systems comes an increased demand for performance. Quantum optimal control (QOC) provides a direct solution to a number of existing challenges as well as a basis for proposed future applications. Together with a swift review of QOC strategies, quantum sensing, and other relevant quantum technology applications of nitrogen-vacancy (NV) centers in diamond, the authors give the necessary background to summarize recent advancements in the field of QOC assisted quantum applications with NV centers in diamond

Cumulant Expansions and the Spin-Boson Problem

The dynamics of the dissipative two-level system at zero temperature is studied using three different cumulant expansion techniques. The relative merits and drawbacks of each technique are discussed. It is found that a new technique, the non-crossing cumulant expansion, appears to embody the virtues of the more standard cumulant methods.Comment: 26 pages, LaTe

Igniting homogeneous nucleation

Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-D\"oring kinetic equations with two different models of discrete diffusivity: the classic Turnbull-Fisher formula and an expression describing thermally driven growth of the nucleus. The latter diffusivity yields time lags for nucleation which are much closer to values measured in experiments with disilicate glasses. After an initial stage in which the number of monomers decreases, many clusters of small size are produced and a continuous size distribution is created. During the second era, nucleii are increasing steadily in size in such a way that their distribution appears as a wave front advancing towards the critical size for steady nucleation. The nucleation rate at critical size is negligible during this era. After the wave front reaches critical size, it ignites the creation of supercritical clusters at a rate that increases monotonically until its steady value is reached. Analytical formulas for the transient nucleation rate and the time lag are obtained that improve classical ones and compare very well with direct numerical solutions.Comment: 32 pages, 6 figures, to appear in Phys. Rev.

Sensitivity analysis of circadian entrainment in the space of phase response curves

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations.Comment: 22 pages, 8 figures. Correction of a mistake in Definition 2.1. arXiv admin note: text overlap with arXiv:1206.414

Influence of batch or fed-batch growth on Staphylococcus epidermidis biofilm formation

Aims: To make a quantitative evaluation of the differences in biofilm formation by Staphylococcus epidermidis using batch and fed-batch growth systems and to correlate this with production of the major biofilm polysaccharide, poly-N-acetyl glucosamine (PNAG). Methods and Results: Dry weight measurements of biofilms formed in batch and fed-batch conditions were compared with haemagglutination titres, which measure the amount of PNAG produced. Strains grown in batch systems developed less biofilm than when grown in fed-batch systems. A good correlation was found between the amount of biofilm formed in fed-batch systems and the haemagglutination titres. Conclusions: Differences in biofilm formation and PNAG production by S. epidermidis are dependent on the availability of nutrients, with higher availability correlating with more biofilm and PNAG production. Significance of and Impact of the Study: Comparisons of the formation of biofilms by S. epidermidis are dependent on choosing an appropriate biofilm growth system. Comparability or disparity of conclusions among different investigations will be strongly influenced by which mode S. epidermidis biofilms are formed.NIH - grant AI 46706.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) - POCTI/ESP/42688/2001, SFRH/BD/8676/2002