Thermodynamical Properties of Hall Systems

We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the presence of an electromagnetic field and quantum statistical mechanically investigate its basic features. Solving the eigenvalue equation, we analytically derive the energy levels and the corresponding wavefunctions. These will be used, at low temperature and weak electric field, to determine the thermodynamical potential \Omega^{nc} and related physical quantities. Varying \Omega^{nc} with respect to the non-commutativity parameter \theta, we define a new function that can be interpreted as a \Omega^{nc} density. Evaluating the particle number, we show that the Hall conductivity of the system is \theta-dependent. This allows us to make contact with quantum Hall effect by offering different interpretations. We study the high temperature regime and discuss the magnetism of the system. We finally show that at \theta=2l_B^2, the system is sharing some common features with the Laughlin theory.Comment: 20 pages, misprints correcte

The semi-presidential system of Cape Verde: the relationship between the executive and the legislative powers = O sistema semi-presidencialista caboverdiano: a relação entre os poderes executivo e legislativo

e article analyses the relationship established between the executive and legislative powers in the Cape Verdean government system where researchers seek to understand it, taking into account their theoretical and constitutional setting practice. It should be noted the prominence of the debate and studies undertaken to understand how the scienti c academy seeks to eradicate this problem. Two issues are relevant in this debate: the rst reporting to the theoretical and constitutional con guration of Cape Verdean government system and the other to its policy and legislative practice. Keywords: Cape Verde. Semi-presidential System. Systems of Government. Legislative and Executive Powers.O artigo procura analisar a relação que se estabelece entre o poder executivo e legislativo no sistema de governo cabo-verdiano, onde Investigadores buscam compreendê-lo, tendo em conta a sua con guração prática, teórica e constitucional. Há que realçar a proeminência do debate e dos estudos realizados no sentido de compreender como é que a academia cientí ca procura debelar esta problemática. Duas questões são pertinentes neste debate: a primeira refere-se à con guração teórico-constitucional do sistema de governo cabo-verdiano e a outra à prática política e legislativa. Palavras-chave: Cabo Verde. Sistema Semi-presidencialista. Sistemas de Governo. Poder legislativo e Poder Executivo

Optimization of Material Contrast for Efficient FIB‐SEM Tomography of Solid Oxide Fuel Cells

Focused ion beam (FIB) – scanning electron microscopy (SEM) serial sectioning tomography has become an important tool for three‐dimensional microstructure reconstruction of solid oxide fuel cells (SOFC) to obtain an understanding of fabrication‐related effects and SOFC performance. By sequential FIB milling and SEM imaging a stack of cross‐section images across all functional SOFC layers was generated covering a large volume of 3.5·10$^{4}$ μm$^{3}$. One crucial step is image segmentation where regions with different image intensities are assigned to different material phases within the SOFC. To analyze all relevant SOFC materials, it was up to now mandatory to acquire several images by scanning the same region with different imaging parameters because sufficient material contrast could otherwise not be achieved. In this work we obtained high‐contast SEM images from a single scan to reconstract all functional SOFC layers consisting of a Ni/Y$_{2}$O$_{3}$‐doped ZrO$_{2}$ (YDZ) cermet anode, YDZ electrolyte and (La,Sr)MnO$_{3}$/YDZ cathode. This was possible by using different, simultaneous read‐out detectors installed in a state‐of‐the‐art scanning electron microscope. In addition, we used a deterministic approach for the optimization of imaging parameters by employing Monte Carlo simulations rather than trial‐and‐error tests. We also studied the effect of detection geometry, detecting angle range and detector type

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.Comment: !5 pages, no figure

Permafrost degradation at two monitored palsa mires in north-west Finland

Palsas and peat plateaus are expected to disappear from many regions, including Finnish Lapland. However, detailed long-term monitoring data of the degradation process on palsas are scarce. Here, we present the results of the aerial photography time series analysis (1959–2021), annual real-time kinematic (RTK) GNSS and active layer monitoring (2007–2021), and annual unoccupied aerial system surveys (2016–2021) at two palsa sites (Peera and Laassaniemi, 68∘ N) located in north-west Finland. We analysed temporal trends of palsa degradation and their relation to climate using linear regression. At both sites, the decrease in palsa area by −77 % to −90 % since 1959 and height by −16 % to −49 % since 2007 indicate substantial permafrost degradation throughout the study periods. The area loss rates are mainly connected to winter air temperature changes at Peera and winter precipitation changes at Laassaniemi. The active layer thickness (ALT) has varied annually between 2007 and 2021 with no significant trend and is related mainly to the number of very warm days during summer, autumn rainfall of previous year, and snow depths at Peera. At Laassaniemi, the ALT is weakly related to climate and has been decreasing in the middle part of the palsa during the past 8 years despite the continuous decrease in palsa volume. Our findings imply that the ALT in the inner parts of palsas do not necessarily reflect the overall permafrost conditions and underline the importance of surface position monitoring alongside the active layer measurements. The results also showed a negative relationship between the ALT and snow cover onset, indicating the complexity of climate–permafrost feedbacks in palsa mires.</p

The transverse magnetoresistance of the two-dimensional chiral metal

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.Comment: submitted to Phys Rev

Optimization of entanglement witnesses

An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an optimal way. We show how to optimize general EW, and then we particularize our results to the non-decomposable ones; the latter are those that can detect positive partial transpose entangled states (PPTES). We also present a method to systematically construct and optimize this last class of operators based on the existence of ``edge'' PPTES, i.e. states that violate the range separability criterion [Phys. Lett. A{\bf 232}, 333 (1997)] in an extreme manner. This method also permits the systematic construction of non-decomposable positive maps (PM). Our results lead to a novel sufficient condition for entanglement in terms of non-decomposable EW and PM. Finally, we illustrate our results by constructing optimal EW acting on H=\C^2\otimes \C^4. The corresponding PM constitute the first examples of PM with minimal ``qubit'' domain, or - equivalently - minimal hermitian conjugate codomain.Comment: 18 pages, two figures, minor change

Variation of elastic scattering across a quantum well

The Drude scattering times of electrons in two subbands of a parabolic quantum well have been studied at constant electron sheet density and different positions of the electron distribution along the growth direction. The scattering times obtained by magnetotransport measurements decrease as the electrons are displaced towards the well edges, although the lowest-subband density increases. By comparing the measurements with calculations of the scattering times of a two-subband system, new information on the location of the relevant scatterers and the anisotropy of intersubband scattering is obtained. It is found that the scattering time of electrons in the lower subband depends sensitively on the position of the scatterers, which also explains the measured dependence of the scattering on the carrier density. The measurements indicate segregation of scatterers from the substrate side towards the quantum well during growth.Comment: 4 pages, 4 figure