The single-correlator conformal bootstrap is solved numerically for several values of dimension 4 > d > 2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained over the entire range of dimensions with up to four-decimal precision and then compared with several existing results. The conformal dimensions of leading-twist fields are also determined up to high spin, and their d-dependence shows how the conformal states rearrange themselves around d = 2.2 for matching the Virasoro conformal blocks in the d = 2 limit. The decoupling of states at the Ising point is studied for 3 > d > 2 and the vanishing of one structure constant at d = 3 is found to persist till d = 2 where it corresponds to a Virasoro null-vector condition. arXiv:1811.07751v2 [hep-th]
We present a detailed microscopic study of edge excitations for n filled Landau levels. We show that the higher-level wavefunctions possess a non-trivial radial dependence that should be integrated over for properly defining the edge conformal field theory. This analysis let us clarify the role of the electron orbital spin s in the edge theory and to discuss its universality, thus providing a further instance of the bulk-boundary correspondence. We find that the values s i for each level, i = 1, . . . , n, parameterize a Casimir effect or chemical potential shift that could be experimentally observed. These results are generalized to fractional and hierarchical fillings by exploiting the W-infinity symmetry of incompressible Hall fluids.
This article presents the design and the experimental tests of a bioinspired robot mimicking the cownose ray. These fish swim by moving their large and flat pectoral fins, creating a wave that pushes backward the surrounding water so that the fish is propelled forward due to momentum conservation. The robot inspired by these animals has a rigid central body, housing motors, batteries, and electronics, and flexible pectoral fins made of silicone rubber. Each of them is actuated by a servomotor driving a link inside the leading edge, and the traveling wave is reproduced thanks to the flexibility of the fin itself. In addition to the pectoral fins, two small rigid caudal fins are present to improve the robot’s maneuverability. The robot has been designed, built, and tested underwater, and the experiments have shown that the locomotion principle is valid and that the robot is able to swim forward, perform left and right turns, and do floating or diving maneuvers.
The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.