A new orthogonalization procedure with an extremal property

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the Schweinler- Wigner procedure, is democratic and is endowed with an extremal property is suggested.Comment: 7 pages, latex, no figures, To appear in J. Phys

Constitutional Analogies in the International Legal System

This Article explores issues at the frontier of international law and constitutional law. It considers five key structural and systemic challenges that the international legal system now faces: (1) decentralization and disaggregation; (2) normative and institutional hierarchies; (3) compliance and enforcement; (4) exit and escape; and (5) democracy and legitimacy. Each of these issues raises questions of governance, institutional design, and allocation of authority paralleling the questions that domestic legal systems have answered in constitutional terms. For each of these issues, I survey the international legal landscape and consider the salience of potential analogies to domestic constitutions, drawing upon and extending the writings of international legal scholars and international relations theorists. I also offer some preliminary thoughts about why some treaties and institutions, but not others, more readily lend themselves to analysis in constitutional terms. And I distinguish those legal and political issues that may generate useful insights for scholars studying the growing intersections of international and constitutional law from other areas that may be more resistant to constitutional analogies

A study of transport suppression in an undoped AlGaAs/GaAs quantum dot single-electron transistor

We report a study of transport blockade features in a quantum dot single-electron transistor, based on an undoped AlGaAs/GaAs heterostructure. We observe suppression of transport through the ground state of the dot, as well as negative differential conductance at finite source-drain bias. The temperature and magnetic field dependence of these features indicate the couplings between the leads and the quantum dot states are suppressed. We attribute this to two possible mechanisms: spin effects which determine whether a particular charge transition is allowed based on the change in total spin, and the interference effects that arise from coherent tunneling of electrons in the dot

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.Comment: To be published in Classical and Quantum Gravit

Cognition-Enhancing Drugs: Can We Say No?

Normative analysis of cognition-enhancing drugs frequently weighs the liberty interests of drug users against egalitarian commitments to a level playing field. Yet those who would refuse to engage in neuroenhancement may well find their liberty to do so limited in a society where such drugs are widespread. To the extent that unvarnished emotional responses are world-disclosive, neurocosmetic practices also threaten to provide a form of faulty data to their users. This essay examines underappreciated liberty-based and epistemic rationales for regulating cognition-enhancing drugs

Primordial Entropy Production and Lambda-driven Inflation from Quantum Einstein Gravity

We review recent work on renormalization group (RG) improved cosmologies based upon a RG trajectory of Quantum Einstein Gravity (QEG) with realistic parameter values. In particular we argue that QEG effects can account for the entire entropy of the present Universe in the massless sector and give rise to a phase of inflationary expansion. This phase is a pure quantum effect and requires no classical inflaton field.Comment: 12 pages, 4 figures, IGCG-07 Pun

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in J.Phys.A (Fast Track Communication

Non-spiky density of states of an icosahedral quasicrystal

The density of states of the ideal three-dimensional Penrose tiling, a quasicrystalline model, is calculated with a resolution of 10 meV. It is not spiky. This falsifies theoretical predictions so far, that spikes of width 10-20 meV are generic for the density of states of quasicrystals, and it confirms recent experimental findings. The qualitative difference between our results and previous calculations is partly explained by the small number of k points that has usually been included in the evaluation of the density of states of periodic approximants of quasicrystals. It is also shown that both the density of states of a small approximant of the three-dimensional Penrose tiling and the density of states of the ideal two-dimensional Penrose tiling do have spiky features, which also partly explains earlier predictions.Comment: 8 pages, 4 figures. Changes in this version: longer introduction, details of figures shown in inset

Scale-dependent metric and causal structures in Quantum Einstein Gravity

Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) and the resulting families of resolution dependent metrics are discussed. The status of scale dependent vs. scale independent diffeomorphisms is clarified, and the difference between isometries implemented by scale dependent and independent Killing vectors is explained. A concept of scale dependent causality is proposed and illustrated by various simple examples. The possibility of assigning an "intrinsic length" to objects in a QEG spacetime is also discussed.Comment: 52 page

Tkachenko modes and quantum melting of Josephson junction type of vortex array in rotating Bose-Einstein condensate

Using path integral formalism, we show that the Abrikosov-Tkachenko vortex lattice may equivalently be understood as an array of Josephson junctions. The Tkachenko modes are found to be basically equivalent to the low energy excitations (Goldstone modes) of an ordered state. The calculated frequencies are in very good agreement with recent experimental data. Calculations of the fluctuations of the relative displacements of the vortices show that vortex melting is a result of quantum fluctuations around the ordered state due to the low energy excitations (Tkachenko modes)and occurs when the ratio of the kinectic energy to the potential energy of the vortex lattice is 0.001.Comment: revised paper 11 pages with 2 figures, all in Pdf forma