The role of background independence for asymptotic safety in Quantum Einstein Gravity

We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular, the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the?) key prerequisite for the existence of a non-Gaussian RG fixed point and the renormalizability of QEG.     

High‐pressure syntheses of α‐RE2B4O9 (RE = Sm,Ho), with a structure type displaying edge‐sharing BO4 tetrahedra

The compounds α‐RE₂B₄O₉, with RE = Sm (disamarium tetraborate) and Ho (diholmium tetraborate), were synthesized under conditions of high pressure and high temperature in a Walker‐type multianvil apparatus, at 7.5 GPa and 1323 K for α‐Sm₂B₄O₉ and at 10 GPa and 1323 K for α‐Ho₂B₄O₉. The crystal structures were determined from single‐crystal X‐ray diffraction data collected at room temperature. The structures are isotypic with the already known α‐RE₂B₄O₉ (RE = Eu–Dy) phases, displaying the new structural motif of edge‐sharing BO₄ tetrahedra next to the known motif of corner‐sharing BO₄ tetrahedra. As the end members of this isotypic series, the two title compounds mark the borders of the stability field of the appearance of edge‐sharing BO₄ tetrahedra.     

Comparative Analysis of Electron‐Density and Electron‐Localization Function for Dinuclear Manganese Complexes with Bridging Boron‐ and Carbon‐Centered Ligands

Bonding in borylene‐, carbene‐, and vinylidene‐bridged dinuclear manganese complexes [MnCp(CO)₂]₂X (X=B‐tBu, B=NMe₂, CH₂, C?CH₂) has been compared by analyses based on quantum theory of atoms in molecules (QTAIM), on the electron‐localization function (ELF), and by natural‐population analyses. All of the density functional theory based analyses agree on the absence of a significant direct Mn? Mn bond in these complexes and confirm a dominance of delocalized bonding via the bridging ligand. Interestingly, however, the topology of both charge density and ELF related to the Mn‐bridge‐Mn bonding depend qualitatively on the chosen density functional (except for the methylene‐bridged complex, which exhibits only one three‐center‐bonding attractor both in ??²ρ and in ELF). While gradient‐corrected functionals provide a picture with localized two‐center X? Mn bonding, increasing exact‐exchange admixture in hybrid functionals concentrates charge below the bridging atom and suggests a three‐center bonding situation. For example, the bridging boron ligands may be described either as substituted boranes (e.g., at BLYP or BP86 levels) or as true bridging borylenes (e.g., at BHLYP level). This dependence on the theoretical level appears to derive from a bifurcation between two different bonding situations and is discussed in terms of charge transfer between X and Mn, and in the context of self‐interaction errors exhibited by popular functionals.     

Casimir edge effects

We compute Casimir forces in open geometries with edges, involving parallel as well as perpendicular semi-infinite plates. We focus on Casimir configurations which are governed by a unique dimensional scaling law with a universal coefficient. With the aid of worldline numerics, we determine this coefficient for various geometries for the case of scalar-field fluctuations with Dirichlet boundary conditions. Our results facilitate an estimate of the systematic error induced by the edges of finite plates, for instance, in a standard parallel-plate experiment. The Casimir edge effects for this case can be reformulated as an increase of the effective area of the configuration.     

Site‐Resolved Observation of Vibrational Energy Transfer Using a Genetically Encoded Ultrafast Heater

Allosteric information transfer in proteins has been linked to distinct vibrational energy transfer (VET) pathways in a number of theoretical studies. Experimental evidence for such pathways, however, is sparse because site‐selective injection of vibrational energy into a protein, that is, localized heating, is required for their investigation. Here, we solved this problem by the site‐specific incorporation of the non‐canonical amino acid β‐(1‐azulenyl)‐l ‐alanine (AzAla) through genetic code expansion. As an exception to Kasha's rule, AzAla undergoes ultrafast internal conversion and heating after S₁ excitation while upon S₂ excitation, it serves as a fluorescent label. We equipped PDZ3, a protein interaction domain of postsynaptic density protein 95, with this ultrafast heater at two distinct positions. We indeed observed VET from the incorporation sites in the protein to a bound peptide ligand on the picosecond timescale by ultrafast IR spectroscopy. This approach based on genetically encoded AzAla paves the way for detailed studies of VET and its role in a wide range of proteins.