Condensates in group field theory

In der Theorie der Gruppenfeldtheorie (GFT) der Quantengravitation löst sich das übliche Raum-Zeit-Kontinuum mikroskopisch in diskrete Bausteine auf. Eine große Herausforderung besteht darin, wie man aus diesen fundamentalen nicht-raumzeitlichen Freiheitsgraden die auf dem Raum-Zeit-Kontinuum basierende Physik extrahieren kann. Im Allgemeinen besteht jeder makroskopische Bereich des Raumes aus zahlreichen Bausteinen, und er kann aus Mean-Field Kondensatzuständen extrahiert werden. Innerhalb von GFT, welche über $SU(2)$-Gruppen definiert ist, kann das Kondensat durch Spins unterschiedlicher Darstellungen charakterisiert werden. Im kosmologischen Sektor kann man das Kondensat jedoch von einem bestimmten Typ wählen, dessen Spins identisch sind. Dadurch kann die kombinatorische Struktur der GFT-Wechselwirkung ignoriert werden, was zu einer effektiv einfacheren Dynamik führt. Wir bezeichnen verschiedene Spins als Moden, und wir extrahieren die kosmologische Entwicklung unter Beitrag mehrerer Moden. Zu früher kosmologischer Zeit herrscht Dominanz von kinetischen Termen, die zu Beschleunigungsexpansionen unmittelbar nach dem Bounce führen. Diese frühen Beschleunigungen sind aber auch mit alen Moden nicht von langer Dauer. Wechselwirkungsterme sind für die späte Beschleunigung notwendig. Insbesondere bei zwei Kondensatmoden können wir eine phantomähnliche Expansion rein quanten-gravitativen Ursprungs erhalten, auch ohne Phantom-Materie. Ein solches Verhalten kann durch die effektive equation of state aufgezeigt werden, aus der wir auch die ungefähre Position des Phantom-Übergangs, der im Ein-Moden-Fall fehlt, erhalten. Dieser erfolgt bei einer niedrigen Rotverschiebung, weswegen die Einbeziehung der zweiten Mode nur zu späten Zeiten zu Modifizierungen führt. Solche Modifikationen können den aktuellen Hubble-Wert $H_0$ , der aus Daten abgeleitet wurde, erhöhen und somit zur Entlastung der $H_0$-Spannung aufgrund von Quantengravitationseffekten beitragen. Darüber hinaus können wir durch die Berücksichtigung inhomogener Störungen in Kondensaten des Boulatov-Modells, einer 3d-GFT, die Dynamik eines Materiefeldes in Form einer generalisierten Version des Amit-Roginsky (AR)-Modells erhalten. Im Gegensatz zum kosmologischen Sektor berücksichtigen wir dabei die kombinatorischen Strukturen der Wechselwirkungsterme. Hierfür betrachten eine Klasse von Lösungen, um die perturbiert werden soll, und wählen passende Störungen für den Angleich an die AR Freiheitsgrade. Die AR-Dynamik emergiert im Kondensat unter zwei zusätzlichen Bedingungen, und die resultierende Wirkung ist eine Summe von AR-Modellen mit verschiedenen Spins. Diese Verallgemeinerung bricht melonische Dominanz im large-N Grenzwert, aber kann in bestimmten Näherungen wiederhergestellt werden.As a theory of quantum gravity, in group field theory (GFT) the usual spacetime dissolves microscopically into discretized building blocks. A major challenge is to understand how the familiar laws of physics based on continuous spacetime can emerge from these fundamental, non-spatio-temporal elements. Generally, any macroscopic region of the spacetime consists numerous number of building blocks, and the spacetime continuum can be extracted from condensate states at the mean field level. In GFT over $SU(2)$ group, the corresponding condensate can be characterized by spins of different representations. For the cosmological sector, one can choose the condensate as a particular type whose spins are identical, such that the combinatorial structure of the GFT interaction can be ignored, which provides a simpler dynamics effectively. Different spins are referred to as ‘modes’, and we want to study the cosmological evolution when multiple modes contribute. At early times, the dynamics of GFT is primarily governed by kinetic terms, resulting in accelerated expansion right after the cosmic bounce. However, these early-time accelerations are not long-lasting even when all modes are taken into account. Late-time acceleration requires interaction terms, and in particular, when we consider two condensate modes, we can obtain phantom-like evolution that arises purely from quantum gravity, without any phantom matter. Such behaviour can be revealed through the effective equation of state, from which the position of phantom crossing can be determined approximately. The crossing occurs at a low red shift, which indicates that the inclusion of the second mode modifies the single mode evolution only at late times. Such modifications can increase the current Hubble value $H_0$ inferred from data, which shed some lights in alleviating the $H_0$ tension based on quantum gravity effects. Furthermore, by considering inhomogeneous perturbations over the condensates of the Boulatov model, a 3d GFT, we are able to get the dynamics of a matter field, in the form of a generalized version of the Amit-Roginsky (AR) model. Unlike the cosmological sector, the combinatorial structures of the interaction terms will be taken into account. We consider a class of solutions to the equation of motion, which serves as the condensate function to be perturbed, and choose suitable forms of perturbations to match the AR degrees of freedom. The AR dynamics will emerge when the condensate satisfies two additional conditions, and the resulting action will be a summation over the original AR model of different spins. This generalization breaks the melonic dominance in the large-N limit, but it can be restored under certain approximations

Late Time Acceleration of the Universe from Quantum Gravity

We show that the accelerating expansion phase of the universe can emerge from the group field theory formalism, a candidate theory of quantum gravity. The cosmological evolution can be extracted from condensate states using the mean field approximation, in a form of modified FLRW equations. By introducing an effective equation of state w, we can reveal the relevant features of the evolution and show that, with the proper choice of the parameters, w will approach −1, leading to an accelerating phase dominated by the cosmological constant effectively

Aerodynamic Shape Optimization with Grassmannian Shape Parameterization Method

The conventional method of optimizing the aerodynamic performance of an airfoil heavily depends on the confines of the design space. The design variables create a non-normalized space that is fragmented into several different clusters of airfoils. An approach that is data-driven and deforms airfoils over a Grassmannian submanifold is utilized in the work that is being presented here. The affine deformation, which includes camber and thickness, can be uncoupled from the method that is currently in use, and the operations that are performed on the airfoil shape can be made smooth enough to prevent unreasonable shapes from being produced. The CST method is also a part of the current study so that a comparison can be made between the two. A new method to describe the airfoil geometries over the Grassmannian space was generated using a dataset that contained 7007 different shapes of airfoils. These two methods are used to parameterize the subsonic (NACA0012) and transonic (RAE2822) airfoils, and the new method cuts the number of design variables from twelve to six, resulting in a reduction in overall complexity. The findings demonstrate that the new method maintains a high degree of consistency regardless of the flow conditions

Generalised Amit-Roginsky model from perturbations of 3d quantum gravity

International audienceA generalised Amit-Roginsky vector model in flat space is obtained as the effective dynamics of pertubations around a classical solution of the Boulatov group field theory for 3d euclidean quantum gravity, extended to include additional matter degrees of freedom. By further restricting the type of perturbations, the original Amit-Roginsky model can be obtained. This result suggests a general link (and possibly a unified framework) between two types of tensorial quantum field theories: quantum geometric group field theories and tensorial models for random geometry, on one hand, and melonic-dominated vector and tensorial models in flat space, such as the Amit-Roginsky model (and the SYK model), on the other hand

Effect of Long-Term Nitrogen and Phosphorus Additions on Understory Plant Nutrients in a Primary Tropical Forest

Humid tropical forests are commonly characterized as N-rich but P-deficient. Increased N deposition may drive N saturation and aggravate P limitation in tropical forests. Thus, P addition is proposed to mitigate the negative effects of N deposition by stimulating N cycling. However, little is known regarding the effect of altered N and P supply on the nutrient status of understory plants in tropical forests, which is critical for predicting the consequences of disturbed nutrient cycles. We assessed the responses of N concentration, P concentration, and N:P ratios of seven understory species to N and P addition in an 8-year fertilization experiment in a primary forest in south China. The results showed that N addition had no effect on plant N concentration, P concentration, and N:P ratios for most species. In contrast, P addition significantly increased P concentration, and decreased N:P ratios but had no effect on plant N concentration. The magnitude of P concentration responses to P addition largely depended on the types of organs and species. The increased P was more concentrated in the fine roots and branches than in the leaves. The gymnospermous liana Gnetum montanum Markgr. had particularly lower foliar N: P (~9.8) and was much more responsive to P addition than the other species studied. These results indicate that most plants are saturated in N but have great potential to restore P in primary tropical forests. N deposition does not necessarily aggravate plant P deficiency, and P addition does not increase the retention of deposited N by increasing the N concentration. In the long term, P inputs may alter the community composition in tropical forests owing to species-specific responses

Design, fabrication and testing of CVD diamond detectors with high performance

A single crystal diamond (SCD) detector and a polycrystalline diamond (PCD) detector have been designed and fabricated using electronic grade CVD diamond. The fabricated detectors were tested for their dark current and X-ray photocurrent. It was found that the SCD and PCD detectors have superb signal to noise ratios (SNR) under X-ray irradiation from an Ag target with 10kV and 40kV accelerating voltage, 2000 and 7000 respectively for the SCD detector and 550 and 2000 for the PCD detector. The performance of these detectors using an 241Am α source was tested under different bias voltages and the results were benchmarked against a commercial SCD detector. The typical rise time of an α event in both of the fabricated detectors are about 1.2ns. The fabricated SCD detector has a 3.7% net energy resolution while that of the commercial detector is about 3.9%. The pulse height spectra are integrated and fitted to obtain the charge collection efficiency. For the fabricated SCD detector, this value is above 97% at bias 200V or beyond, which is 1-2% higher than that of the commercial detector at the same voltage. Finally, the fabricated PCD detector can also detect the presence of α particle although it only has a continuous and decreasing energy spectrum under α radiation. These results fully reveal that the fabricated SCD detector has good performance as a multifunctional detector for both X-ray and α radiation, and show great potential as neutron spectrometer as well