Edge Currents for Quantum Hall Systems, I. One-Edge, Unbounded Geometries

Devices exhibiting the integer quantum Hall effect can be modeled by one-electron Schroedinger operators describing the planar motion of an electron in a perpendicular, constant magnetic field, and under the influence of an electrostatic potential. The electron motion is confined to unbounded subsets of the plane by confining potential barriers. The edges of the confining potential barrier create edge currents. In this, the first of two papers, we prove explicit lower bounds on the edge currents associated with one-edge, unbounded geometries formed by various confining potentials. This work extends some known results that we review. The edge currents are carried by states with energy localized between any two Landau levels. These one-edge geometries describe the electron confined to certain unbounded regions in the plane obtained by deforming half-plane regions. We prove that the currents are stable under various potential perturbations, provided the perturbations are suitably small relative to the magnetic field strength, including perturbations by random potentials. For these cases of one-edge geometries, the existence of, and the estimates on, the edge currents imply that the corresponding Hamiltonian has intervals of absolutely continuous spectrum. In the second paper of this series, we consider the edge currents associated with two-edge geometries describing bounded, cylinder-like regions, and unbounded, strip-like, regions.Comment: 68 page

Magnetic transport in a straight parabolic channel

We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists

Assessing the impact of observations on ocean forecasts and reanalyses: Part 2, Regional applications

The value of global (e.g., altimetry, satellite sea-surface temperature, Argo) and regional (e.g., radars, gliders, instrumented mammals, airborne profiles, biogeochemical) observation-types for monitoring the mesoscale ocean circulation and biogeochemistry is demonstrated using a suite of global and regional prediction systems and remotely-sensed data. A range of techniques is used to demonstrate the value of different observation-types to regional systems and the benefit of high- resolution and adaptive sampling for monitoring the mesoscale circulation. The techniques include Observing System Experiments, Observing System Simulation Experiments, adjoint sensitivities, representer matrix spectrum, observation footprints, information content and spectral analysis. It is shown that local errors in global and basin-scale systems can be significantly reduced when assimilating observations from regional observing systems

On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with a potential $V(x)$ converging to different limits $V_{\ell}$ and $V_{r}$ as $x \to -\infty$ and $x \to +\infty$ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $|x| \to \infty$ ($V_\ell = V_r$). We show that it remains true in the anisotropic case $V_\ell \not = V_r$, i.e. we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.Comment: 48 pages, 1 figur

A step back on the conservation of a highly threatened species: opposite signs of recovery on Pinna nobilis population from Mar Menor lagoon

The endemic species Pinna nobilis is the most endangered Mediterranean bivalve, facing nearly extinction all over the Mediterranean Sea, hosting its last reservoirs in highly impacted coastal lagoons. Thus, knowledge about the populations' conservation status in these ecosystems is essential. In 2019, the Mar Menor lagoon’s population was considered as a highly vulnerable population (Nebot-Colomer et al., 2021) due to several ecological disasters. The present study represents a continuation of the previous work, which aims to evaluate the resilience of the population, by assessing its reproductive success and maintenance of the population. To do so, between 2019 to 2022, we installed between 23-45 larvae collectors, monitored 13 permanent individual’s plots, and conducted visual searches and censuses. Overall, densities remained stable over years, although the number of individuals alive monitored in permanent plots decrease each year. Moreover, none of the methodologies carried out detected the incorporation of recruits in the population. Our results pointed out to opposite signs of recovery of the species, increasing its vulnerability to future disturbances. Therefore, urgent management and conservation actions focused on restoring the ecosystem and protecting P. nobilis individuals are needed to avoid this population extinction

Asymptotic Lower Bounds for a class of Schroedinger Equations

We shall study the following initial value problem: \begin{equation}{\bf i}\partial_t u - \Delta u + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times {\mathbf R}^n, \end{equation} $$u(0)=f,$$ where $V(x)$ is a real short--range potential, whose radial derivative satisfies some supplementary assumptions. More precisely we shall present a family of identities satisfied by the solutions to the previous Cauchy problem. As a by--product of these identities we deduce some uniqueness results and a lower bound for the so called local smoothing which becomes an identity in a precise asymptotic sense.Comment: 24 pages. to appear on Comm. Math. Phy

Pelagic habitat and offspring survival in the eastern stock of Atlantic bluefin tuna

In this manuscript, we test how an understanding of geographical variation in larval fitness in relation to temperature and habitat use could be a useful method to improve our understanding of recruitment and develop better indices of annual recruitment. On the basis of the assumption that growth and survival of tuna larvae are influenced by temperature, we have developed a potential larval survival index for Atlantic bluefin tuna (Thunnus thynnus) by combining empirical data from egg and larval rearing experiments with temperature data from hydrodynamic models. The experiments were designed to test the full range of temperature variability that bluefin larvae would experience in the field and provide a mechanistic understanding of the processes driving egg and larval survival. We then developed a biological model using the temperature-related growth expressions and a size-dependent survival function for the larvae. The biological model was applied to a time-series of spatially explicit temperature data for the western Mediterranean from the Strait of Gibraltar to 6 E, which includes the major recognized bluefin tuna eastern stock spawning area, the Balearic Sea. Our results show that areas with high probabilities of larval survival coincide with those that would be considered as optimal based on other data sources (ichthyoplankton surveys, spawning female locations from commercial fisheries data, and adult tracking data). However, evidence of spawning has been found in areas with suboptimal thermal habitats, as predicted by the model, which we discuss regarding sampling effort and salinity fronts. There was a good match between the survival index and recruitment indices from standardized CPUE fisheries data. These results have implications for our understanding of the recruitment process of the eastern stock of Atlantic bluefin tuna, since they suggest that the combined effects of temporal and spatial variability of the environment drive recruitment success, which has important implications for the management of the species.Versión del editor2,27

High-resolution observations in the western Mediterranean Sea: the REP14-MED experiment

The observational part of the REP14-MED experiment was conducted in June 2014 in the Sardo-Balearic Basin west of Sardinia (western Mediterranean Sea). Two research vessels collected high-resolution oceanographic data by means of hydrographic casts, towed systems, and underway measurements. In addition, a vast amount of data was provided by a fleet of 11 ocean gliders, time series were available from moored instruments, and information on Lagrangian flow patterns was obtained from surface drifters and one profiling float. The spatial resolution of the observations encompasses a spectrum over 4 orders of magnitude from (10¹ m) to (10⁵ m), and the time series from the moored instruments cover a spectral range of 5 orders from (10¹ s) to (10⁶ s). The objective of this article is to provide an overview of the huge data set which has been utilised by various studies, focusing on (i) water masses and circulation, (ii) operational forecasting, (iii) data assimilation, (iv) variability of the ocean, and (v) new payloads for gliders