Entanglement entropy of fermions in any dimension and the Widom conjecture

We show that entanglement entropy of free fermions scales faster then area law, as opposed to the scaling $L^{d-1}$ for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the entanglement entropy of free fermions in any dimension $d$, $S\sim c(\partial\Gamma,\partial\Omega)\cdot L^{d-1}\log L$ as the size of a subsystem $L\to\infty$, where $\partial\Gamma$ is the Fermi surface and $\partial\Omega$ is the boundary of the region in real space. The expression for the constant $c(\partial\Gamma,\partial\Omega)$ is based on a conjecture due to H. Widom. We prove that a similar expression holds for the particle number fluctuations and use it to prove a two sided estimates on the entropy $S$.Comment: Final versio

Lower order terms in Szego type limit theorems on Zoll manifolds

This is a detailed version of the paper math.FA/0212273. The main motivation for this work was to find an explicit formula for a "Szego-regularized" determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold. The idea of the Szego-regularization was suggested by V. Guillemin and K. Okikiolu. They have computed the second term in a Szego type expansion on a Zoll manifold of an arbitrary dimension. In the present work we compute the third asymptotic term in any dimension. In the case of dimension 2, our formula gives the above mentioned expression for the Szego-redularized determinant of a zeroth order PsDO. The proof uses a new combinatorial identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This identity is related to the distribution of the maximum of a random walk with i.i.d. steps on the real line. The proof of this combinatorial identity together with historical remarks and a discussion of probabilistic and algebraic connections has been published separately.Comment: 39 pages, full version, submitte

Electrical characterization and nanoscale surface morphology of optimized Ti/Al/Ta/Au ohmic contact for AlGaN/GaN HEMT

Good ohmic contacts with low contact resistance, smooth surface morphology, and a well-defined edge profile are essential to ensure optimal device performances for the AlGaN/GaN high electron mobility transistors [HEMTs]. A tantalum [Ta] metal layer and an SiNx thin film were used for the first time as an effective diffusion barrier and encapsulation layer in the standard Ti/Al/metal/Au ohmic metallization scheme in order to obtain high quality ohmic contacts with a focus on the thickness of Ta and SiNx. It is found that the Ta thickness is the dominant factor affecting the contact resistance, while the SiNx thickness affects the surface morphology significantly. An optimized Ti/Al/Ta/Au ohmic contact including a 40-nm thick Ta barrier layer and a 50-nm thick SiNx encapsulation layer is preferred when compared with the other conventional ohmic contact stacks as it produces a low contact resistance of around 7.27 × 10-7 Ω·cm2 and an ultra-low nanoscale surface morphology with a root mean square deviation of around 10 nm. Results from the proposed study play an important role in obtaining excellent ohmic contact formation in the fabrication of AlGaN/GaN HEMTs

Atomic Force Microscopy Study of the Kinetic Roughening in Nanostructured Gold Films on SiO2

Dynamic scaling behavior has been observed during the room-temperature growth of sputtered Au films on SiO2using the atomic force microscopy technique. By the analyses of the dependence of the roughness, σ, of the surface roughness power,P(f), and of the correlation length,ξ, on the film thickness,h, the roughness exponent,α = 0.9 ± 0.1, the growth exponent,β = 0.3 ± 0.1, and the dynamic scaling exponent,z = 3.0 ± 0.1 were independently obtained. These values suggest that the sputtering deposition of Au on SiO2at room temperature belongs to a conservative growth process in which the Au grain boundary diffusion plays a dominant role

Thermodynamic Properties of Supported and Embedded Metallic Nanocrystals: Gold on/in SiO2

We report on the calculations of the cohesive energy, melting temperature and vacancy formation energy for Au nanocrystals with different size supported on and embedded in SiO2. The calculations are performed crossing our previous data on the surface free energy of the supported and embedded nanocrystals with the theoretical surface-area-difference model developed by W. H. Qi for the description of the size-dependent thermodynamics properties of low-dimensional solid-state systems. Such calculations are employed as a function of the nanocrystals size and surface energy. For nanocrystals supported on SiO2, as results of the calculations, we obtain, for a fixed nanocrystal size, an almost constant cohesive energy, melting temperature and vacancy formation energy as a function of their surface energy; instead, for those embedded in SiO2, they decreases when the nanocrystal surface free energy increases. Furthermore, the cohesive energy, melting temperature and vacancy formation energy increase when the nanocrystal size increases: for the nanocrystals on SiO2, they tend to the values of the bulk Au; for the nanocrystals in SiO2 in correspondence to sufficiently small values of their surface energy, they are greater than the bulk values. In the case of the melting temperature, this phenomenon corresponds to the experimentally well-known superheating process

Effect of surrounding environment on atomic structure and equilibrium shape of growing nanocrystals: gold in/on SiO2

We report on the equilibrium shape and atomic structure of thermally-processed Au nanocrystals (NCs) as determined by high resolution transmission electron microscopy (TEM). The NCs were either deposited on SiO2surface or embedded in SiO2layer. Quantitative data on the NCs surface free energy were obtained via the inverse Wulff construction. Nanocrystals inside the SiO2layer are defect-free and maintain a symmetrical equilibrium shape during the growth. Nanocrystals on SiO2surface exhibit asymmetrical equilibrium shape that is characterized by the introduction of twins and more complex atomic defects above a critical size. The observed differences in the equilibrium shape and atomic structure evolution of growing NCs in and on SiO2is explained in terms of evolution in isotropic/anisotropic environment making the surface free energy function angular and/or radial symmetric/asymmetric affecting the rotational/translational invariance of the surface stress tensor

A meta-review of evidence on heart failure disease management programs: the challenges of describing and synthesizing evidence on complex interventions

Background: Despite favourable results from past meta-analyses, some recent large trials have not found Heart Failure (HF) disease management programs to be beneficial. To explore reasons for this, we evaluated evidence from existing meta-analyses. Methods: Systematic review incorporating meta-review was used. We selected meta-analyses of randomized controlled trials published after 1995 in English that examined the effects of HF disease management programs on key outcomes. Databases searched: MEDLINE, EMBASE, Cochrane Database of Systematic Reviews (CDSR), DARE, NHS EED, NHS HTA, Ageline, AMED, Scopus, Web of Science and CINAHL; cited references, experts and existing reviews were also searched. Results: 15 meta-analyses were identified containing a mean of 18.5 randomized trials of HF interventions +/- 10.1 (range: 6 to 36). Overall quality of the meta-analyses was very mixed (Mean AMSTAR Score = 6.4 +/- 1.9; range 2-9). Reporting inadequacies were widespread around populations, intervention components, settings and characteristics, comparison, and comparator groups. Heterogeneity (statistical, clinical, and methodological) was not taken into account sufficiently when drawing conclusions from pooled analyses. Conclusions: Meta-analyses of heart failure disease management programs have promising findings but often fail to report key characteristics of populations, interventions, and comparisons. Existing reviews are of mixed quality and do not adequately take account of program complexity and heterogeneity