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

Tracing CP-violation in Lepton Flavor Violating Muon Decays

Although the Lepton Flavor Violating (LFV) decay $\mu^+\to e^+ \gamma$ is forbidden in the Standard Model (SM), it can take place within various theories beyond the SM. If the branching ratio of this decay saturates its present bound [{\it i.e.,} Br$(\mu^+ \to e^+\gamma)\sim 10^{-11}$], the forthcoming experiments can measure the branching ratio with high precision and consequently yield information on the sources of LFV. In this letter, we show that for polarized $\mu^+$, by studying the angular distribution of the transversely polarized positron and linearly polarized photon we can derive information on the CP-violating sources beyond those in the SM. We also study the angular distribution of the final particles in the decay $\mu^+\to e^+_1 e^- e^+_2$ where $e^+_1$ is defined to be the more energetic positron. We show that transversely polarized $e_1^+$ can provide information on a certain combination of the CP-violating phases of the underlying theory which would be lost by averaging over the spin of $e^+_1$.Comment: 6 pages, 2 figure

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

The stability of the O(N) invariant fixed point in three dimensions

We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo simulations. It is well know that there is a critical value $2<N_c<4$ below which the O(N) fixed point is stable and above which the cubic fixed point becomes the stable one. While we cannot exclude that $N_c<3$, as recently claimed by Kleinert and collaborators, our analysis strongly suggests that $N_c$ coincides with 3.Comment: latex file of 18 pages plus three ps figure

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

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

Improving the Efficiency of an Ideal Heat Engine: The Quantum Afterburner

By using a laser and maser in tandem, it is possible to obtain laser action in the hot exhaust gases involved in heat engine operation. Such a "quantum afterburner" involves the internal quantum states of working gas atoms or molecules as well as the techniques of cavity quantum electrodynamics and is therefore in the domain of quantum thermodynamics. As an example, it is shown that Otto cycle engine performance can be improved beyond that of the "ideal" Otto heat engine.Comment: 5 pages, 3 figure

Quantum error correction of coherent errors by randomization

A general error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomization of static imperfections in a many-qubit system by the repeated application of Pauli operators which change the computational basis. This Pauli-Random-Error-Correction (PAREC)-method eliminates coherent errors produced by static imperfections and increases significantly the maximum time over which realistic quantum computations can be performed reliably. Furthermore, it does not require redundancy so that all physical qubits involved can be used for logical purposes.Comment: revtex 4 pages, 3 fig