Symbolic calculus on the time-frequency half-plane

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.Comment: 25 pages, Latex, minor changes and more references; to be published in the "Journal of Mathematical Physics" (special issue on "Wavelet and Time-Frequency Analysis"

Why Christians Should Not Be Kaneans about Freedom

Abstract: In this paper we argue that Robert Kane’s theory of free will cannot accommodate the possibility of a sinless individual who faces morally significant choices because a sinless agent cannot voluntarily accord value to an immoral desire, and we argue that Kane’s theory requires this. Since the Jesus of the historic Christian tradition is held to be sinless, we think Christians should reject Kane’s theory because it seems irreconcilable with historic Christian Christology. We consider two objections to our argument and argue that both fail

Conductance beyond the Landauer limit and charge pumping in quantum wires

Periodically driven systems, which can be described by Floquet theory, have been proposed to show characteristic behavior that is distinct from static Hamiltonians. Floquet theory proposes to describe such periodically driven systems in terms of states that are indexed by a photon number in addition to the usual Hilbert space of the system. We propose a way to measure directly this additional Floquet degree of freedom by the measurement of the DC conductance of a single channel quantum point contact. Specifically, we show that a single channel wire augmented with a grating structure when irradiated with microwave radiation can show a DC conductance above the limit of one conductance quantum set by the Landauer formula. Another interesting feature of the proposed system is that being non-adiabatic in character, it can be used to pump a strong gate-voltage dependent photo-current even with linearly polarized radiation.Comment: 9 pages; 3 figures: Final published version; includes minor revisions from the last versio

Inelastic Neutron and X-ray Scattering from Incommensurate Magnetic Systems

Neutrons and X-rays are powerful probes for studying magnetic and lattice excitations in strongly correlated materials over very wide ranges of momentum and energy transfers. In the focus of the present work are the incommensurate magnetic systems MnSi and Cr. Under application of a magnetic field, helically ordered MnSi transforms into a weak itinerant ferromagnet. Using polarized neutrons we demonstrate that the Stoner excitations are spin flip excitations. The amplitude (longitudinal) fluctuations associated with the magnon modes are already strong far away from T_C. Interestingly, even the non spin flip excitations associated with the Stoner modes are observable. In Cr, we have observed Kohn anomalies in the phonon spectrum at those incommensurate positions in reciprocal space, where the spin density wave is observed. The corresponding phonon and magnon modes are not coupled. In addition, an anomalous softening of a transverse phonon branch along the N-H zone boundary line is observed that is caused by strong electron phonon coupling. High resolution neutron scattering indicate that the low energy Fincher-Burke excitations may rather correspond to localized modes in momentum and energy and not to propagating collective modes. Finally, we demonstrate that in the near future it may become feasible to investigate excitations in very small samples thus allowing to measure the dynamics of strongly correlated materials under extreme conditions and in the vicinity of quantum phase transitions

Concept for controlled transverse emittance transfer within a linac ion beam

For injection of beams into circular machines with different horizontal and vertical emittance acceptance, the injection efficiency can be increased if these beams are flat, i.e. if they feature unequal transverse emittances. Generation of flat electron beams is well known and has been demonstrated already in beam experiments. It was proposed also for ion beams that were generated in an Electron Cyclotron-Resonance (ECR) source. We introduce an extension of the method to beams that underwent charge state stripping without requiring their generation inside an ECR source. Results from multi-particle simulations are presented to demonstrate the validity of the method.Comment: 23 pages (preprint style), 14 Figures, submitted to PRST-A

Carbon Nanotube Based Bearing for Rotational Motions

We report the fabrication of a nanoelectromechanical system consisting of a plate rotating around a multiwalled nanotube bearing. The motion is possible thanks to the low intershell friction. Indeed, the nanotube has been engineered so that the sliding happens between different shells. The plate rotation is activated electrostatically with stator electrodes. The static friction force is estimated at $\approx 2\cdot10^{-15}$ N/\AA$^2$.Comment: 4 pages, 3 figure