Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that, even without electric potential, the spectrum has positive measure if the magnetic field is a perturbation of a constant one.Comment: 17 page

Perspective: tobacco manufacturers are now compensating states for smoking-related costs: how will this affect the economy?

Smoking out the social and economic benefits of the 1998 tobacco settlement for Massachusetts.Tobacco industry ; Medical care, Cost of

Strain bursts in plastically deforming Molybdenum micro- and nanopillars

Plastic deformation of micron and sub-micron scale specimens is characterized by intermittent sequences of large strain bursts (dislocation avalanches) which are separated by regions of near-elastic loading. In the present investigation we perform a statistical characterization of strain bursts observed in stress-controlled compressive deformation of monocrystalline Molybdenum micropillars. We characterize the bursts in terms of the associated elongation increments and peak deformation rates, and demonstrate that these quantities follow power-law distributions that do not depend on specimen orientation or stress rate. We also investigate the statistics of stress increments in between the bursts, which are found to be Weibull distributed and exhibit a characteristic size effect. We discuss our findings in view of observations of deformation bursts in other materials, such as face-centered cubic and hexagonal metals.Comment: 14 pages, 8 figures, submitted to Phil Ma

On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.Comment: 29 pages, 9 figures submitted to Journal of Statistical Physics (2003

The Economic Impacts of the Tobacco Settlement

Recent litigation against major tobacco companies culminated in a Master Settlement Agreement' (MSA) under which the participating companies agreed to compensate most states for Medicaid expenses. We outline the terms of the settlement and analyze whether it was a move toward economic efficiency using data from Massachusetts. Medicaid spending will fall, but only a modest amount ($0.1 billion). The efficiency issue turns mainly on the treatment of health benefits from reduced smoking induced by the settlement. We conclude that the settlement was a move towards economic efficiency.

Phase Rotation, Cooling And Acceleration Of Muon Beams: A Comparison Of Different Approaches

Experimental and theoretical activities are underway at CERN with the aim of examining the feasibility of a very-high-flux neutrino source. In the present scheme, a high-power proton beam (some 4 MW) bombards a target where pions are produced. The pions are collected and decay to muons under controlled optical condition. The muons are cooled and accelerated to a final energy of 50 GeV before being injected into a decay ring where they decay under well-defined conditions of energy and emittance. We present the most challenging parts of the whole scenario, the muon capture, the ionisation-cooling and the first stage of the muon acceleration. Different schemes, their performance and the technical challenges are compared.Comment: LINAC 2000 CONFERENCE, paper ID No. THC1

General duality for abelian-group-valued statistical-mechanics models

We introduce a general class of statistical-mechanics models, taking values in an abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of ``variables'' and a set of ``interactions''. A Gibbs factor is associated to each variable and to each interaction. We introduce a duality transformation for systems in this class. The duality exchanges the abelian group with its dual, the Gibbs factors with their Fourier transforms, and the interactions with the variables. High (low) couplings in the interaction terms are mapped into low (high) couplings in the one-body terms. The idea is that our class of systems extends the one for which the classical procedure 'a la Kramers and Wannier holds, up to include randomness into the pattern of interaction. We introduce and study some physical examples: a random Gaussian Model, a random Potts-like model, and a random variant of discrete scalar QED. We shortly describe the consequence of duality for each example.Comment: 26 pages, 2 Postscript figure

Coil combination of multichannel MRSI data at 7 T: MUSICAL

The goal of this study was to evaluate a new method of combining multi-channel 1H MRSI data by direct use of a matching imaging scan as a reference, rather than computing sensitivity maps. Seven healthy volunteers were measured on a 7-T MR scanner using a head coil with a 32-channel array coil for receive-only and a volume coil for receive/transmit. The accuracy of prediction of the phase of the 1H MRSI data with a fast imaging pre-scan was investigated with the volume coil. The array coil 1H MRSI data were combined using matching imaging data as coil combination weights. The signal-to-noise ratio (SNR), spectral quality, metabolic map quality and Cramér–Rao lower bounds were then compared with the data obtained by two standard methods, i.e. using sensitivity maps and the first free induction decay (FID) data point. Additional noise decorrelation was performed to further optimize the SNR gain. The new combination method improved significantly the SNR (+29%), overall spectral quality and visual appearance of metabolic maps, and lowered the Cramér–Rao lower bounds (−34%), compared with the combination method based on the first FID data point. The results were similar to those obtained by the combination method using sensitivity maps, but the new method increased the SNR slightly (+1.7%), decreased the algorithm complexity, required no reference coil and pre-phased all spectra correctly prior to spectral processing. Noise decorrelation further increased the SNR by 13%. The proposed method is a fast, robust and simple way to improve the coil combination in 1H MRSI of the human brain at 7 T, and could be extended to other 1H MRSI techniques. © 2013 The Authors. NMR in Biomedicine published by John Wiley & Sons, Ltd

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include