Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach

y formally diagonalizing with accuracy $\hbar$ the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase corrections, and therefore confirm the validity of the Liouville theorem. We show that both the position and momentum operators acquire a Berry-phase dependence, leading to a non-canonical Hamiltonian dynamics. The equations of motion turn out to be identical to the ones previously derived in the context of electron wave-packets dynamics.Comment: 4 page

From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006

Sclerochronological studies in the humboldt current system, a highly variable ecosystem

The Humboldt Current that bathes the west coast of South America is affected by different influences at daily to decadal periodicities. Environmental influences such as upwelling or coastal trapped waves as well as climate influences such as El Nino southern oscillation and Pacific decadal oscillation events interact and modify the thermonutricline depth of this Humboldt Current System. The position of this thermonutricline plays a key role in Humboldt Current System functioning by driving sea surface temperature (SST) and primary production variations. As filter feeders, bivalves are particularly affected by SST and primary production, and their shells can provide information about these two environmental factors. Using sclerochronology, we studied three bivalve species from different ecological niches living along the Peruvian-Chilean coast. Depending on the species, thick or thin sections, etched or not, were studied using an optical microscope. Increment thicknesses were measured at the surface of the shell and/or in cross-section. Moreover, the mineralogical composition of the different layers of the studied shells was determined on thin sections by Fourier transform infrared spectroscopic analyses. Growth results were then interpreted tentatively in terms of environmental variations. For the free-living, short-lived Pectinidae Argopecten purpuratus, the daily growth rhythm is linked to the solar period whereas growth amplitude seems to be related to the occurrence of spawning events, probably triggered by specific water temperature patterns. tidal regime and SST seem to be the major environmental parameters that govern shell growth rhythms and/or increment thickness for two nearshore species-the Mytilidae Choromytilus chorus and the Veneridae Eurhomalea rufa-which grow more slowly and have a life span longer than A. purpuratus, and have a strong potential for paleo-environmental and paleo-El Nino southern oscillation reconstruction. These results need to be confirmed studying multiple shells to quantify individual growth variations and to enhance the significance of the findings on the different environmental parameters recorded in the growth patterns of the South American bivalve species studied

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.

Fourfold oscillations and anomalous magnetic irreversibility of magnetoresistance in the non-metallic regime of Pr1.85Ce0.15CuO4

Using magnetoresistance measurements as a function of applied magnetic field and its direction of application, we present sharp angular-dependent magnetoresistance oscillations for the electron-doped cuprates in their low-temperature non-metallic regime. The presence of irreversibility in the magnetoresistance measurements and the related strong anisotropy of the field dependence for different in-plane magnetic field orientations indicate that magnetic domains play an important role for the determination of electronic properties. These domains are likely related to the stripe phase reported previously in hole-doped cuprates.Comment: 11 pages, 5 figure

Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution

A generalized Peierls substitution which takes into account a Berry phase term must be considered for the semiclassical treatment of electrons in a magnetic field. This substitution turns out to be an essential element for the correct determination of the semiclassical equations of motion as well as for the semiclassical Bohr-Sommerfeld quantization condition for energy levels. A general expression for the cross-sectional area is derived and used as an illustration for the calculation of the energy levels of Bloch and Dirac electrons

Workspace and Singularity analysis of a Delta like family robot

Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{\"o}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.Comment: 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France. 201

Cracking the code of oscillatory activity

Neural oscillations are ubiquitous measurements of cognitive processes and dynamic routing and gating of information. The fundamental and so far unresolved problem for neuroscience remains to understand how oscillatory activity in the brain codes information for human cognition. In a biologically relevant cognitive task, we instructed six human observers to categorize facial expressions of emotion while we measured the observers' EEG. We combined state-of-the-art stimulus control with statistical information theory analysis to quantify how the three parameters of oscillations (i.e., power, phase, and frequency) code the visual information relevant for behavior in a cognitive task. We make three points: First, we demonstrate that phase codes considerably more information (2.4 times) relating to the cognitive task than power. Second, we show that the conjunction of power and phase coding reflects detailed visual features relevant for behavioral response-that is, features of facial expressions predicted by behavior. Third, we demonstrate, in analogy to communication technology, that oscillatory frequencies in the brain multiplex the coding of visual features, increasing coding capacity. Together, our findings about the fundamental coding properties of neural oscillations will redirect the research agenda in neuroscience by establishing the differential role of frequency, phase, and amplitude in coding behaviorally relevant information in the brai

The structural and chemical basis of temporary adhesion in the sea star Asterina gibbosa

Background: Marine biological adhesives are a promising source of inspiration for biomedical and industrial applications. Nevertheless, natural adhesives and especially temporary adhesion systems are mostly unexplored. Sea stars are able to repeatedly attach and detach their hydraulic tube feet. This ability is based on a duo-gland system and, upon detachment, the adhesive material stays behind on the substrate as a 'footprint'. In recent years, characterization of sea star temporary adhesion has been focussed on the forcipulatid species Asterias rubens. Results: We investigated the temporary adhesion system in the distantly related valvatid species Asterina gibbosa. The morphology of tube feet was described using histological sections, transmission-, and scanning electron microscopy. Ultrastructural investigations revealed two adhesive gland cell types that both form electron-dense secretory granules with a more lucid outer rim and one de-adhesive gland cell type with homogenous granules. The footprints comprised a meshwork on top of a thin layer. This topography was consistently observed using various methods like scanning electron microscopy, 3D confocal interference microscopy, atomic force microscopy, and light microscopy with crystal violet staining. Additionally, we tested 24 commercially available lectins and two antibodies for their ability to label the adhesive epidermis and footprints. Out of 15 lectins labelling structures in the area of the duo-gland adhesive system, only one also labelled footprints indicating the presence of glycoconjugates with α-linked mannose in the secreted material. Conclusion: Despite the distant relationship between the two sea star species, the morphology of tube feet and topography of footprints in A. gibbosa shared many features with the previously described findings in A. rubens. These similarities might be due to the adaptation to a benthic life on rocky intertidal areas. Lectin- and immuno-labelling indicated similarities but also some differences in adhesive composition between the two species. Further research on the temporary adhesive of A. gibbosa will allow the identification of conserved motifs in sea star adhesion and might facilitate the development of biomimetic, reversible glues.</p