The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics ...takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type.
•The Asymptotic Safety scenario in quantum gravity is explored.•A bi-metric generalization of the Einstein–Hilbert truncation is investigated.•We find that Background Independence can coexist with Asymptotic Safety.•RG trajectories restoring (background-quantum) split-symmetry are constructed.•The degree of validity of single-metric truncations is critically assessed.
Nanowires are conventionally assumed to grow via the vapor-liquid-solid process, in which material from the vapor is incorporated into the growing nanowire via a liquid catalyst, commonly a ...low--melting point eutectic alloy. However, nanowires have been observed to grow below the eutectic temperature, and the state of the catalyst remains controversial. Using in situ microscopy, we showed that, for the classic Ge/Au system, nanowire growth can occur below the eutectic temperature with either liquid or solid catalysts at the same temperature. We found, unexpectedly, that the catalyst state depends on the growth pressure and thermal history. We suggest that these phenomena may be due to kinetic enrichment of the eutectic alloy composition and expect these results to be relevant for other nanowire systems.
The past decade has seen a resurgence of interest in the supply security of mineral raw materials. A key to the current debate is the concept of 'criticality'. The present article reviews the ...criticality concept, as well as the methodologies used in its assessment, including a critical evaluation of their validity in view of classical risk theory. Furthermore, it discusses a number of risks present in global raw materials markets that are not captured by most criticality assessments. Proposed measures for the alleviation of these risks are also presented. We find that current assessments of raw material criticality are fundamentally flawed in several ways. This is mostly due to a lack of adherence to risk theory, and highly limits their applicability. Many of the raw materials generally identified as critical are probably not critical. Still, the flaws of current assessments do not mean that the general issue of supply security can simply be ignored. Rather, it implies that new assessments are required. While the basic theoretical framework for such assessments is outlined in this review, detailed method development will require a major collaborative effort between different disciplines along the raw materials value chain. In the opinion of the authors, the greatest longer-term challenge in the raw materials sector is to stop, or counteract the effects of, the escalation of unit energy costs of production. This issue is particularly pressing due to its close link with the renewable energy transition, requiring more metal and mineral raw materials per unit energy produced. The solution to this problem will require coordinated policy action, as well as the collaboration of scientists from many different fields-with physics, as well as the materials and earth sciences in the lead.
We have formed compositionally abrupt interfaces in silicon-germanium (Si-Ge) and Si-SiGe heterostructure nanowires by using solid aluminum-gold alloy catalyst particles rather than the conventional ...liquid semiconductor-metal eutectic droplets. We demonstrated single interfaces that are defect-free and close to atomically abrupt, as well as quantum dots (i.e., Ge layers tens of atomic planes thick) embedded within Si wires. Real-time imaging of growth kinetics reveals that a low solubility of Si and Ge in the solid particle accounts for the interfacial abruptness. Solid catalysts that can form functional group IV nanowire-based structures may yield an extended range of electronic applications.
The amygdala is composed of multiple nuclei with unique functions and connections in the limbic system and to the rest of the brain. However, standard in vivo neuroimaging tools to automatically ...delineate the amygdala into its multiple nuclei are still rare. By scanning postmortem specimens at high resolution (100–150µm) at 7T field strength (n = 10), we were able to visualize and label nine amygdala nuclei (anterior amygdaloid, cortico-amygdaloid transition area; basal, lateral, accessory basal, central, cortical medial, paralaminar nuclei). We created an atlas from these labels using a recently developed atlas building algorithm based on Bayesian inference. This atlas, which will be released as part of FreeSurfer, can be used to automatically segment nine amygdala nuclei from a standard resolution structural MR image. We applied this atlas to two publicly available datasets (ADNI and ABIDE) with standard resolution T1 data, used individual volumetric data of the amygdala nuclei as the measure and found that our atlas i) discriminates between Alzheimer's disease participants and age-matched control participants with 84% accuracy (AUC=0.915), and ii) discriminates between individuals with autism and age-, sex- and IQ-matched neurotypically developed control participants with 59.5% accuracy (AUC=0.59). For both datasets, the new ex vivo atlas significantly outperformed (all p < .05) estimations of the whole amygdala derived from the segmentation in FreeSurfer 5.1 (ADNI: 75%, ABIDE: 54% accuracy), as well as classification based on whole amygdala volume (using the sum of all amygdala nuclei volumes; ADNI: 81%, ABIDE: 55% accuracy). This new atlas and the segmentation tools that utilize it will provide neuroimaging researchers with the ability to explore the function and connectivity of the human amygdala nuclei with unprecedented detail in healthy adults as well as those with neurodevelopmental and neurodegenerative disorders.
•We visualized 9 nuclei boundaries (anterior amygdaloid area, cortico-amygdaloid transition area; basal, lateral, accessory basal, central, cortical medial, paralaminar nuclei) using ultra-high-resolution ex vivo imaging.•Nuclei were consistent across cases and raters.•We built a segmentation atlas of the amygdala nuclei, which will be distributed with FreeSurfer.•Atlas was applied to 2 datasets and showed higher discriminability of Alzheimer's & autism than previously possible.•The atlas will provide neuroimaging researchers with the ability to test nucleus function with greater spatial specificity.
We observe in situ the vapor-liquid-solid (VLS) growth of Si nanowires, in UHV-CVD using Au catalyst. The nanowire sidewalls exhibit periodic sawtooth faceting, reflecting an oscillatory growth ...process. We interpret the facet alternation as resulting from the interplay of the geometry and surface energies of the wire and liquid droplet. Such faceting may be present in any VLS growth system in which there are no stable orientations parallel to the growth direction. The sawtooth structure has important implications for electronic mobility and scattering in nanowire devices.
We measured the nucleation and growth kinetics of solid silicon (Si) from liquid gold-silicon (AuSi) catalyst particles as the Si supersaturation increased, which is the first step of the ...vapor-liquid-solid growth of nanowires. Quantitative measurements agree well with a kinetic model, providing a unified picture of the growth process. Nucleation is heterogeneous, occurring consistently at the edge of the AuSi droplet, yet it is intrinsic and highly reproducible. We studied the critical supersaturation required for nucleation and found no observable size effects, even for systems down to 12 nanometers in diameter. For applications in nanoscale technology, the reproducibility is essential, heterogeneity promises greater control of nucleation, and the absence of strong size effects simplifies process design.
Nanowire growth by the vapour-liquid-solid (VLS) process enables a high level of control over nanowire composition, diameter, growth direction, branching and kinking, periodic twinning, and crystal ...structure. The tremendous impact of VLS-grown nanowires is due to this structural versatility, generating applications ranging from solid-state lighting and single-photon sources to thermoelectric devices. Here, we show that the morphology of these nanostructures can be further tailored by using the liquid droplets that catalyse nanowire growth as a 'mixing bowl', in which growth materials are sequentially supplied to nucleate new phases. Growing within the liquid, these phases adopt the shape of faceted nanocrystals that are then incorporated into the nanowires by further growth. We demonstrate this concept by epitaxially incorporating metal-silicide nanocrystals into Si nanowires with defect-free interfaces, and discuss how this process can be generalized to create complex nanowire-based heterostructures.
We present few-femtosecond shadowgraphic snapshots taken during the nonlinear evolution of the plasma wave in a laser wakefield accelerator with transverse synchronized few-cycle probe pulses. These ...snapshots can be directly associated with the electron density distribution within the plasma wave and give quantitative information about its size and shape. Our results show that self-injection of electrons into the first plasma-wave period is induced by a lengthening of the first plasma period. Three-dimensional particle-in-cell simulations support our observations.
We use real-time observations of the growth of copper-catalyzed silicon nanowires to determine the nanowire growth mechanism directly and to quantify the growth kinetics of individual wires. ...Nanowires were grown in a transmission electron microscope using chemical vapor deposition on a copper-coated Si substrate. We show that the initial reaction is the formation of a silicide, η′-Cu3Si, and that this solid silicide remains on the wire tips during growth so that growth is by the vapor−solid−solid mechanism. Individual wire directions and growth rates are related to the details of orientation relation and catalyst shape, leading to a rich morphology compared to vapor−liquid−solid grown nanowires. Furthermore, growth occurs by ledge propagation at the silicide/silicon interface, and the ledge propagation kinetics suggest that the solubility of precursor atoms in the catalyst is small, which is relevant to the fabrication of abrupt heterojunctions in nanowires.
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