Pure scaling operators at the integer quantum Hall plateau transition

Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multi-fractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlations functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the CFT prediction for a 3-point function involving two primary fields.Comment: Published version, 4 pages, 3 figure

Use of remotely-derived bathymetry for modelling biomass in marine environments

The paper presents results on the influence of geometric attributes of satellite-derived raster bathymetric data, namely the General Bathymetric Charts of the Oceans, on spatial statistical modelling of marine biomass. In the initial experiment, both the resolution and projection of the raster dataset are taken into account. It was found that, independently of the equal-area projection chosen for the analysis, the calculated areas are very similar, and the differences between them are insignificant. Likewise, any variation in the raster resolution did not change the computed area. Although the differences were shown to be insignificant, for the subsequent analysis we selected the cylindrical equal area projection, as it implies rectangular spatial extent, along with the automatically derived resolution. Then, in the second experiment, we focused on demersal fish biomass data acquired from trawl samples taken from the western parts of ICES Sub-area VII, near the sea floor. The aforementioned investigation into processing bathymetric data allowed us to build various statistical models that account for a relationship between biomass, sea floor topography and geographic location. We fitted a set of generalised additive models and generalised additive mixed models to combinations of trawl data of the roundnose grenadier (Coryphaenoides rupestris) and bathymetry. Using standard statistical techniques—such as analysis of variance, Akaike information criterion, root mean squared error, mean absolute error and cross-validation—we compared the performance of the models and found that depth and latitude may serve as statistically significant explanatory variables for biomass of roundnose grenadier in the study area. However, the results should be interpreted with caution as sampling locations may have an impact on the biomass–depth relationship

How large are present-day heat flux variations across the surface of Mars?

©2016. American Geophysical UnionThe first in situ Martian heat flux measurement to be carried out by the InSight Discovery‐class mission will provide an important baseline to constrain the present‐day heat budget of the planet and, in turn, the thermochemical evolution of its interior. In this study, we estimate the magnitude of surface heat flux heterogeneities in order to assess how the heat flux at the InSight landing site relates to the average heat flux of Mars. To this end, we model the thermal evolution of Mars in a 3‐D spherical geometry and investigate the resulting surface spatial variations of heat flux at the present day. Our models assume a fixed crust with a variable thickness as inferred from gravity and topography data and with radiogenic heat sources as obtained from gamma ray measurements of the surface. We test several mantle parameters and show that the present‐day surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peak‐to peak variations lie between 17.2 and 49.9 mW m−2, with the highest values being associated with the occurrence of prominent mantle plumes. However, strong spatial variations introduced by such plumes remain narrowly confined to a few geographical regions and are unlikely to bias the InSight heat flux measurement. We estimated that the average surface heat flux varies between 23.2 and 27.3 mW m−2, while at the InSight location it lies between 18.8 and 24.2 mW m−2. In most models, elastic lithosphere thickness values exceed 250 km at the north pole, while the south pole values lie well above 110 km

Mercury's low‐degree geoid and topography controlled by insolation‐driven elastic deformation

©2015. American Geophysical UnionMercury experiences an uneven insolation that leads to significant latitudinal and longitudinal variations of its surface temperature. These variations, which are predominantly of spherical harmonic degrees 2 and 4, propagate to depth, imposing a long‐wavelength thermal perturbation throughout the mantle. We computed the accompanying density distribution and used it to calculate the mechanical and gravitational response of a spherical elastic shell overlying a quasi‐hydrostatic mantle. We then compared the resulting geoid and surface deformation at degrees 2 and 4 with Mercury's geoid and topography derived from the MErcury, Surface, Space ENvironment, GEochemistry, and Ranging spacecraft. More than 95% of the data can be accounted for if the thickness of the elastic lithosphere were between 110 and 180 km when the thermal anomaly was imposed. The obtained elastic thickness implies that Mercury became locked into its present 3:2 spin orbit resonance later than about 1 Gyr after planetary formation

Separation of ultrafast spin currents and spin-flip scattering in Co/Cu(001) driven by femtosecond laser excitation via the complex MOKE

Ultrafast magnetization dynamics in metallic heterostructures consists of a combination of local demagnetization in the ferromagnetic constituent and spin-dependent transport contributions within and in between the constituents. Separation of these local and non-local contributions is essential to obtain microscopic understanding and for potential applications of the underlying microscopic processes. By comparing the ultrafast changes of the polarization rotation and ellipticity in the magneto-optical Kerr effect (MOKE) we observe a time-dependent magnetization profile M(z,t) in Co/Cu(001) films by exploiting the effective depth sensitivity of the method. By analyzing the spatio-temporal correlation of these profiles we find that on time scales before hot electron thermalization (<100 fs) the transient magnetization of Co films is governed by spin-dependent transport effects, while after hot electron thermalization (>200 fs) local spin-flip processes dominate.Comment: 9 pages, 6 figures; revised version (title/abstract changed, text/figures from former ancillary file now included in main text, one additional figure, slightly expanded discussion); conclusions remain the same as in previous versio

Charged Particle with Magnetic Moment in the Aharonov-Bohm Potential

We considered a charged quantum mechanical particle with spin ${1\over 2}$ and gyromagnetic ratio $g\ne 2$ in the field af a magnetic string. Whereas the interaction of the charge with the string is the well kown Aharonov-Bohm effect and the contribution of magnetic moment associated with the spin in the case $g=2$ is known to yield an additional scattering and zero modes (one for each flux quantum), an anomaly of the magnetic moment (i.e. $g>2$) leads to bound states. We considered two methods for treating the case $g>2$. \\ The first is the method of self adjoint extension of the corresponding Hamilton operator. It yields one bound state as well as additional scattering. In the second we consider three exactly solvable models for finite flux tubes and take the limit of shrinking its radius to zero. For finite radius, there are $N+1$ bound states ($N$ is the number of flux quanta in the tube).\\ For $R\to 0$ the bound state energies tend to infinity so that this limit is not physical unless $g\to 2$ along with $R\to 0$. Thereby only for fluxes less than unity the results of the method of self adjoint extension are reproduced whereas for larger fluxes $N$ bound states exist and we conclude that this method is not applicable.\\ We discuss the physically interesting case of small but finite radius whereby the natural scale is given by the anomaly of the magnetic moment of the electron $a_e=(g-2)/2\approx 10^{-3}$.Comment: 16 pages, Latex, NTZ-93-0