Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard Lattices

Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.Comment: 5 pages, 3 figure

The Geometry of the Gibbs-Appell Equations and Gauss' Principle of Least Constraint

We present a generalisation of the Gibbs-Appell equations which is valid for general Lagrangians. The general form of the Gibbs-Appell equations is shown to be valid in the case when constraints and external forces are present. In the case when the Lagrangian is the kinetic energy with respect to a Riemannian metric, the Gibbs function is shown to be related to the kinetic energy on the tangent bundle of the configuration manifold with respect to the Sasaki metric. We also make a connection with the Gibbs-Appell equations and Gauss' principle of least constraint in the general case

Ribbon growing method and apparatus

A method and apparatus are described which facilitate the growing of silicon ribbon. A container for molten silicon has a pair of passages in its bottom through which filaments extend to a level above the molten silicon, so as the filaments are pulled up they drag up molten silicon to form a ribbon. A pair of guides surround the filaments along most of the height of the molten silicon, so that the filament contacts only the upper portion of the melt. This permits a filament to be used which tends to contaminate the melt if it is in long term contact with the melt. This arrangement also enables a higher melt to be used without danger that the molten silicon will run out of any bottom hole

The Looming Battle for Control of Multidistrict Litigation in Historical Perspective

2018 marks fifty years since the passage of the Multidistrict Litigation Act. But instead of thoughts of a golden-anniversary celebration, an old Rodney Dangerfield one-liner comes to mind: “[M]y last birthday cake looked like a prairie fire.” Indeed, after a long period of relative obscurity, multidistrict litigation (MDL) has become a subject of major controversy—and not only among scholars of procedure. For a long time, both within and beyond the rarified world of procedure scholars, MDL was perceived as the more technical, less extreme cousin of the class action, which attracted most of the controversy. My goal in this Article is to shed light on the reasons the Multidistrict Litigation Act was constructed as it was and suggest that those engaged in the current debate ask, after becoming informed by available data, whether those reasons have lost any of their currency. I also offer some tenuous predictions about the path forward, recognizing that the prediction business is a dangerous one in the current political climate. First, I review the history to explain why the MDL framework was built without Rules Committee involvement. Then, I fast-forward to the present day and discuss briefly the nascent proposals to either amend the MDL statute or provide for Federal Rules of Civil Procedure for MDL. Finally, I conclude by assessing the current debate and make some suggestions as this debate winds its way forward. In 1968, the small cadre of judges who developed and fought for the MDL statute won the battle for procedural power. Today, fifty years later, the MDL statute continues to operate as they imagined. However, with success comes scrutiny, and what had been settled is now once again up for debate

Catheter Ablation of Tachyarrhythmias in Small Children

An estimated 80,000-100,000 radiofrequency ablation (RFA) procedures are performed in the United States each year.1 Approximately 1% of these are performed on pediatric patients at centers that contribute data to the Pediatric Radiofrequency Registry.2 Previous reports from this registry have demonstrated that RFA can safely and effectively be performed in pediatric patients.3,4 However, patients weighing less than 15 kg have been identified as being at greater risk for complications.3,4 Consequently, there has been great reluctance to perform RFA in small children such that children weighing less than 15 kg only represent approximately 6% of the pediatric RFA experience2 despite the fact that this age group carries the highest incidence of tachycardia, particularly supraventricular tachycardia (SVT).5 Factors other than the risk of complications contribute to the lower incidence of RFA in this group, including the natural history of the most common tachycardias (SVT), technical issues with RFA in small hearts, and the potential unknown long-term effects of RF applications in the maturing myocardium. Conversely, there are several reasons why ablation may be desirable in small children, including greater difficulties with medical management,6,7,8 the higher risk for hemodynamic compromise during tachycardia in infants with congenital heart disease (CHD), and the inability of these small children to effectively communicate their symptoms thereby making it more likely that their symptoms may go unnoticed until the children become more seriously ill. Before ultimately deciding that catheter ablation is indicated in small children, one must consider which tachycardias are likely to be ablated, the clinical presentation of these tachycardias, alternatives to ablation, the relative potential for success or complications, and modifications of the procedure that might reduce the risk of ablation in this group

A Symmetric Product for Vector Fields and its Geometric Meaning

We introduce the notion of geodesic invariance for distributions on manifolds with a linear connection. This is a natural weakening of the concept of a totally geodesic foliation to allow distributions which are not necessarily integrable. To test a distribution for geodesic invariance, we introduce a symmetric, vector field valued product on the set of vector fields on a manifold with a linear connection. This product serves the same purpose for geodesically invariant distributions as the Lie bracket serves for integrable distributions. The relationship of this product with connections in the bundle of linear frames is also discussed. As an application, we investigate geodesically invariant distributions associated with a left-invariant affine connection on a Lie group