Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics

To build genuine generators of the rotations group in noncommutative quantum mechanics, we show that it is necessary to extend the noncommutative parameter $\theta$ to a field operator, which one proves to be only momentum dependent. We find consequently that this field must be obligatorily a dual Dirac monopole in momentum space. Recent experiments in the context of the anomalous Hall effect provide for a monopole in the crystal momentum space. We suggest a connection between the noncommutative field and the Berry curvature in momentum space which is at the origine of the anomalous Hall effect.Comment: 4 page

Non-local heat transport, rotation reversals and up/down impurity density asymmetries in Alcator C-Mod ohmic L-mode plasmas

Several seemingly unrelated effects in Alcator C-Mod ohmic L-mode plasmas are shown to be closely connected: non-local heat transport, core toroidal rotation reversals, energy confinement saturation and up/down impurity density asymmetries. These phenomena all abruptly transform at a critical value of the collisionality. At low densities in the linear ohmic confinement regime, with collisionality ν[subscript *] ≤ 0.35 (evaluated inside of the q = 3/2 surface), heat transport exhibits non-local behaviour, core toroidal rotation is directed co-current, edge impurity density profiles are up/down symmetric and a turbulent feature in core density fluctuations with k[subscript θ] up to 15 cm[superscript −1] (k[subscript θ]ρ[subscript s] ~ 1) is present. At high density/collisionality with saturated ohmic confinement, electron thermal transport is diffusive, core rotation is in the counter-current direction, edge impurity density profiles are up/down asymmetric and the high k[subscript θ] turbulent feature is absent. The rotation reversal stagnation point (just inside of the q = 3/2 surface) coincides with the non-local electron temperature profile inversion radius. All of these observations suggest a possible unification in a model with trapped electron mode prevalence at low collisionality and ion temperature gradient mode domination at high collisionality.United States. Dept. of Energy (Contract DE-FC02-99ER54512)United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program

The Pt isotopes: comparing the Interacting Boson Model with Configuration Mixing and the Extended Consistent-Q formalism

The role of intruder configurations in the description of energy spectra and B(E2) values in the Pt region is analyzed. In particular, we study the differences between Interacting Boson Model calculations with or without the inclusion of intruder states in the even Pt nuclei $^{172-194}$Pt. As a result, it shows that for the description of a subset of the existing experimental data, i.e., energy spectra and absolute B(E2) values up to an excitation energy of about 1.5 MeV, both approaches seem to be equally valid. We explain these similarities between both model spaces through an appropriate mapping. We point out the need for a more extensive comparison, encompassing a data set as broad (and complete) as possible to confront with both theoretical approaches in order to test the detailed structure of the nuclear wave functions.Comment: To be published in NP

Scaling anomaly in cosmic string background

We show that the classical scale symmetry of a particle moving in cosmic string background is broken upon inequivalent quantization of the classical system, leading to anomaly. The consequence of this anomaly is the formation of single bound state in the coupling interval \gamma\in(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter \omega. It has been conjectured that the formation of loosely bound state in cosmic string background may lead to the so called anomalous scattering cross section for the particles, which is usually seen in molecular physics.Comment: 4 pages,1 figur

Observations of Core Toroidal Rotation Reversals in Alcator C-Mod Ohmic L-mode Plasmas

Direction reversals of intrinsic toroidal rotation have been observed in Alcator C-Mod ohmic L-mode plasmas following modest electron density or toroidal magnetic field ramps. The reversal process occurs in the plasma interior, inside of the q = 3/2 surface. For low density plasmas, the rotation is in the co-current direction, and can reverse to the counter-current direction following an increase in the electron density above a certain threshold. Reversals from the co- to counter-current direction are correlated with a sharp decrease in density fluctuations with k(R) >= 2 cm(-1) and with frequencies above 70 kHz. The density at which the rotation reverses increases linearly with plasma current, and decreases with increasing magnetic field. There is a strong correlation between the reversal density and the density at which the global ohmic L-mode energy confinement changes from the linear to the saturated regime

Frequency behavior of Raman coupling coefficient in glasses

Low-frequency Raman coupling coefficient of 11 different glasses is evaluated. It is found that the coupling coefficient demonstrates a universal linear frequency behavior near the boson peak maximum and a superlinear behavior at very low frequencies. The last observation suggests vanishing of the coupling coefficient when frequency tends to zero. The results are discussed in terms of the vibration wavefunction that combines features of localized and extended modes.Comment: 8 pages, 9 figure

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Secular Evolution in Barred Galaxies

A strong bar rotating within a massive halo should lose angular momentum to the halo through dynamical friction, as predicted by Weinberg. We have conducted fully self-consistent, numerical simulations of barred galaxy models with a live halo population and find that bars are indeed braked very rapidly. Specifically, we find that the bar slows sufficiently within a few rotation periods that the distance from the centre to co-rotation is more than twice the semi-major axis of the bar. Observational evidence (meagre) for bar pattern speeds seems to suggest that this ratio typically lies between 1.2 to 1.5 in real galaxies. We consider, a number of possible explanations for this discrepancy between theoretical prediction and observation, and conclude that no conventional alternative seems able to account for it.Comment: To appear in the proceedings of Nobel Symposium 98 "Barred Galaxies and Circumnuclear Activity", edited by Aa. Sandquist, P.O. Lindblad and S. J\"ors\"ater. 17 pages, latex, 6 figure