On avoiding Ostrogradski instabilities within Asymptotic Safety

We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to Ostrogradski ghosts which signal an instability of the system and are therefore dangerous for the consistency of the theory. Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety. Our work then establishes the following picture: upon incorporating higher-derivative terms in the scalar propagator the flow of the gravity-matter system possesses a fixed point structure suitable for Asymptotic Safety. This structure includes an interacting renormalization group fixed point where the Ostrogradski ghosts acquire an infinite mass and decouple from the system. Tracing the flow towards the infrared it is found that there is a subset of complete renormalization group trajectories which lead to stable renormalized propagators. This subset is in one-to-one correspondence to the complete renormalization group trajectories obtained in computations which do not track of the higher-derivative terms. Thus our asymptotically safe gravity-matter systems are not haunted by Ostrogradski ghosts.Comment: 35 pages, 10 figure

Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases

One-dimensional spinor gases with strong delta interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom are described by a spin-chain model with nearest-neighbor interactions. Here, we compute momentum and occupation-number distributions of up to 16 strongly interacting spinor fermions and bosons as a function of their spin imbalance, the strength of an externally applied magnetic field gradient, the length of their spin, and for different excited states of the multiplet. We show that the ground-state momentum distributions resemble those of the corresponding noninteracting systems, apart from flat background distributions, which extend to high momenta. Moreover, we show that the spin order of the spin chain---in particular antiferromagnetic spin order---may be deduced from the momentum and occupation-number distributions of the system. Finally, we present efficient numerical methods for the calculation of the single-particle densities and one-body density matrix elements and of the local exchange coefficients of the spin chain for large systems containing more than 20 strongly interacting particles in arbitrary confining potentials.Comment: See the ancillary files for the Mathematica notebook used to calculate the results of this paper, the derivation of the formula for the one-body density matrix elements, given by Eq. (22), and a table with the local exchange coefficients of up to 60 harmonically trapped particles. A less efficient method for calculating the exchange coefficients was given in the 2nd version of this manuscrip

Dynamic changes in connexin expression correlate with key events in the wound healing process.

Wound healing is a complex process requiring communication for the precise co-ordination of different cell types. The role of extracellular communication through growth factors in the wound healing process has been extensively documented, but the role of direct intercellular communication via gap junctions has scarcely been investigated. We have examined the dynamics of gap junction protein (Connexins 26, 30, 31.1 and 43) expression in the murine epidermis and dermis during wound healing, and we show that connexin expression is extremely plastic between 6 hours and 12 days post-wounding. The immediate response (6 h) to wounding is to downregulate all connexins in the epidermis, but thereafter the expression profile of each connexin changes dramatically. Here, we correlate the changing patterns of connexin expression with key events in the wound healing process

Immuno-electron microscopic quantification of the fucoxanthin chlorophyll a/c binding polypeptides Fcp2, Fcp4, and Fcp6 of Cyclotella cryptica grown under low- and high-light intensities

The diatom Cyclotella cryptica was grown under low- and highintensity white light of 50 and 500 μmol photons m–2 s–1, respectively. Western immunoblotting showed that the diatom adapted its light-harvesting apparatus, giving rise to different amounts of distinct fucoxanthin chlorophyll a/c binding polypeptides (Fcp). The amount of Fcp2 was approximately two-fold higher under low-light than under high-light conditions, whereas the amount of Fcp6 increased four- to five-fold under high-light conditions. For Fcp4, no significant differences were detected in response to either light regime. Cells of Cyclotella grown under high- and low-light intensity were subjected to immunoelectron microscopy. Quantification of the gold label, expressed as gold particles per μm2, confirmed the results obtained by Western immunoblotting. Exposure to low light resulted in the detection of approximately six times more Fcp2-bound gold particles per μm2 in thylakoid membranes, whereas in cells grown under high light the number of Fcp6- bound gold particles increased ten-fold. For Fcp4, similar amounts of gold particles per μm2 were counted under the two light regimes. These immunocytochemical results confirmed molecular data derived from phylogenetic analyses of the sequences of genes encoding fucoxanthin chlorophyll a/c binding polypeptides (fcp genes) and from measurements of steady-state fcp mRNA concentrations. The results show that Fcp2 and Fcp6 accumulate under low- and high-light intensity, respectively, whereas Fcp4 seems to be constitutively synthesized. [Int Microbiol 2006; 9(1):29-36