A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page

Acoustic Phonon-Assisted Resonant Tunneling via Single Impurities

We perform the investigations of the resonant tunneling via impurities embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the $I(V)$ characteristics measured at 30mK, the contribution of individual donors is resolved and the fingerprints of phonon assistance in the tunneling process are seen. The latter is confirmed by detailed analysis of the tunneling rates and the modeling of the resonant tunneling contribution to the current. Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge singularities are observed.Comment: accepted in Phys. Rev.

Track billiards

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the segments and the arcs, the billiards considered have non-zero Lyapunov exponents almost everywhere. These results are then extended to a similar class of of 3-dimensional billiards. Finally, we find that for some subclasses of track billiards, the mechanism generating hyperbolicity is not the defocusing one that requires every infinitesimal beam of parallel rays to defocus after every reflection off of the focusing boundary.Comment: 7 figure

Quantum Metrology Triangle Experiments: A Status Review

Quantum Metrology Triangle experiments combine three quantum electrical effects (the Josephson effect, the quantum Hall effect and the single-electron transport effect) used in metrology. These experiments allow important fundamental consistency tests on the validity of commonly assumed relations between fundamental constants of nature and the quantum electrical effects. This paper reviews the history, results and the present status and perspectives of Quantum Metrology Triangle experiments. It also reflects on the possible implications of results for the knowledge on fundamental constants and the quantum electrical effects.Comment: 36 pages, 8 figure

Protecting Vulnerable Research Subjects in Critical Care Trials: Enhancing the Informed Consent Process and Recommendations for Safeguards

Although critically ill patients represent a vulnerable group of individuals, guidelines in research ethics assert that ethically acceptable research may proceed with such vulnerable subjects if additional safeguards are in place to minimize the risk of harm and exploitation. Such safeguards include the proper obtainment of informed consent that avoids the presence of the therapeutic misconception and the assessment of decisional capacity in critically ill patients recruited for research. Also discussed in this review are additional safeguards for such vulnerable subjects, as well as the issues involved with proxy consent. Heightened awareness to principles of ethics and provision of additional safeguards to enhance protections of vulnerable subjects would help to maintain the public trust in the research endeavor

Highly sensitive nanohall sensors on GaAlAs/GaAs heterojunctions

International audienceWe present an experimental study on the performance of nano-Hall sensors made on the two dimensional electron gaz of a pseudo morphic GaAlAs/GaInAs heterostructures. The active area of the sensor is from sub-micronic scale (down to 500 nm) to 5 microns. Ohmic contacts have micronic size, and a reference sample of 80 micron width has been caracterized as well, as a reference. In our process, we have improved the contacts technology to limit the thermal Shottky noise. Thus although ohmic contacts have small dimensions they have low resistance and do not limit the sensitivity of our nano-sensors. Extensive caracterization of those devices demonstrate a diffusive transport at 300 K, and a magnetic field sensitivity up to 1000 V/T/A. We have focused our attention on the smallest detectable magnetic field in the smallest sensor, and performed a systematic study of the noise measurements. We have measured the excess noise in both the longitudinal configuration and the Hall configuration, as a function of the current. Our noise measurements performed at room temperature in the range [1 Hz-100 kHz] show, at low frequency, an 1/f noise spectrum whose intensity is proportional to the square of the current. We understand our data by the conductivity fluctuations model and we obtain the Hooge parameter for this technology. We demonstrate that the noise intensity is inversely proportional to area of the sensor. Of course reducing the dimensions induces physical limitations but we demonstrate that a magnetic field of few μT can be measured with a micron scale sensor at low frequencies; at higher frequencies, when the thermal noise limits the resolution, the measurement of 300 nT is achievabl