Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force

In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is "driven" by not only the the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.Comment: 4 page

The centripetal force law and the equation of motion for a particle on a curved hypersurface

It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once the fact be taken into consideration, the equation takes that same form as that for centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio

Atomic-Layer-Deposited Al2O3 on Bi2Te3 for Topological Insulator Field-Effect Transistors

We report dual-gate modulation of topological insulator field-effect transistors (TI FETs) made on Bi2Te3 thin flakes with integration of atomic-layer-deposited (ALD) Al2O3 high-k dielectric. Atomic force microscopy study shows that ALD Al2O3 is uniformly grown on this layer-structured channel material. Electrical characterization reveals that the right selection of ALD precursors and the related surface chemistry play a critical role in device performance of Bi2Te3 based TI FETs. We realize both top-gate and bottom-gate control on these devices, and the highest modulation rate of 76.1% is achieved by using simultaneous dual gate control.Comment: 4 pages, 3 figure

The Volcker Rule: A Brief Political History

Today, more than five years after Dodd-Frank was first signed into law, uncertainty surrounds many aspects of the Volcker Rule’s application and ultimate impact on financial markets and bank stability. Many more years will likely pass before that uncertainty is resolved. We demonstrate through a quantitative and qualitative analysis that these difficulties were presaged by the Volcker Rule’s political history. The Volcker Rule -- originally rejected by Congressional lawmakers and economists within the Obama administration as unworkable -- arose as a political concession designed to quiet critics who contended that Dodd-Frank did not do enough to control risky bank activity. But deep divisions about the proper scope of the rule persisted even as the statute was signed into law, ensuring that these debates continued into the rulemaking phase. Efforts to influence the Volcker Rule at the agency level began immediately after presidential signing and persisted until enactment of the final rule. Those expressing an opinion on the rule included affected industry members, academics, public interest groups, private individuals, and state and foreign governments, among others. Systematic analyses of meeting logs and comment letters reveal that much of this activity involved the market making exemption. Specifically, commenters disputed how broadly the exemption should be interpreted and applied, the extent to which limitations on banks’ abilities to make markets would reduce market liquidity, and the likely costs of any such reduction, should it occur