Sigurdur I. Erlingsson

Nucleus-mediated spin-flip transitions in GaAs quantum dots

Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the possibilities to manipulate spin states in the dots. We present here estimations of inelastic spin-flip rates mediated by hyperfine interaction with nuclei. Under general assumptions the nucleus-mediated rate is proportional to the phonon relaxation rate for the corresponding non-spin-flip transitions. The rate can be accelerated in the vicinity of a singlet-triplet excited state crossing. The small proportionality coefficient depends inversely on the number of nuclei in the quantum dot. We compare our results with known mechanisms of spin-flip in GaAs quantum dots.

Investigation of a pavement structural behaviour during spring thaw using falling weight deflectometer

The response of an instrumented flexible pavement structure in southern Sweden, subjected to seasonal freeze–thaw cycles, was investigated during the spring thaw and the recovery periods in 2010. The pavement environmental condition was continuously monitored by measuring subsurface temperature and moisture contents. The mechanical behaviour of the pavement structure was investigated by conducting frequent falling weight deflectometer (FWD) measurements throughout the study period. Considerable decrease in the pavement-bearing capacity was observed as thaw penetrated the pavement structure and consequently moisture content increased in all pavement unbound layers. Highest annual moisture content in the subgrade upper section was registered as thaw penetrated the subgrade and pavement exhibited its weakest structural condition. The analyses of the deflection basin indices and back-calculated unbound layer stiffness from the FWD measurements exhibited a clear correlation with the measured subsurface moisture content. Furthermore, the dissipated energy measured from the FWD time–history data was calculated, exhibiting its highest annual value during the thawing period. Using the back-calculated layer stiffness and moisture measurements in unbound layers, a degree of saturation-based moisture-stiffness model was developed for the granular layer and the subgrade. This model fell on a unique curve showing promising agreement with the laboratory-based model proposed by Mechanistic-Empirical Pavement Design Guide that analytically predicts changes in modulus due to changes in moisture.

Glacial rebound near Vatnajokull, Iceland, studied by GPS campaigns in 1992 and 1996

Abstract Since about 1920 the Vatnajokull ice cap in Iceland has experienced a significant retreat, corresponding to a volume reduction of more than 180 km 3 . With two GPS campaigns in 1992 and 1996 along the southern border of the glacier preliminary results reveal land uplift rates of 1–6 mm/yr, after a one-parameter (bias) fit with recent earth rheology models. The best fit model suggests that the lithosphere in the area is about 30 km thick and the viscosity of the asthenosphere 5 × 10 18 Pa s. The rms fit of uplift rate at all GPS sites is ±1.4 mm/yr. As the GPS data alone cannot provide the absolute uplift rates, the one-parameter fit to the theoretical modelling implies that the absolute rates were estimated by the matching of the GPS data and model. The resulting uplift rate at station Hofn (1 mm/yr) is not consistent with two independent sources, and we therefore conclude that further GPS epoch and permanent GPS site data are needed to confirm the present geodynamic processes near Vatnajokull.

Hyperfine-mediated transitions between a Zeeman split doublet in GaAs quantum dots: The role of the internal field

We consider the hyperfine-mediated transition rate between Zeeman split states of the lowest orbital level in a GaAs quantum dot. We separate the hyperfine Hamiltonian into a part which is diagonal in the orbital states and another one which mixes different orbitals. The diagonal part gives rise to an effective (internal) magnetic field which, in addition to an external magnetic field, determines the Zeeman splitting. Spin-flip transitions in the dots are induced by the orbital mixing part accompanied by an emission of a phonon. We evaluate the rate for different regimes of applied magnetic field and temperature. The rates we find are bigger than the spin–orbit-related rates, provided the external magnetic field is sufficiently low.

Spin susceptibilities, spin densities, and their connection to spin currents

We calculate the frequency-dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interactions. The resonances of the susceptibilities depend on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.

Evolution of localized electron spin in a nuclear spin environment

Motivated by recent interest in the role of the hyperfine interaction in quantum dots we study the dynamics of a localized electron spin coupled to many nuclei. An important feature of the model is that the coupling to an individual nuclear spin depends on its position in the quantum dot. We introduce a semi-classical description of the system valid in the limit of a large number of nuclei and analyze the resulting classical dynamics. Contrary to a natural assumption, the correlation functions of electron spin with an arbitrary initial condition show no decay in time. Rather, they exhibit complicated undamped oscillations. This may be attributed to the fact that the system has many integrals of motion and is close to an integrable one. The ensemble averaged correlation functions do exhibit a slow decay (1/ln(t)) for t -> \infty.

Fast layered elastic response program for the analysis of flexible pavement structures

One of the key components in analysing pavement structural behaviour is the response model which is used to estimate the stresses, strains and displacements of the pavement structure subjected to the existing traffic, taking into account the material properties and prevailing environmental conditions. Multilayer elastic theory (MLET) is often preferred over other methods such as the finite element method, due to its computational performance for repeated applications. A new elastic response analysis program has been developed based on the Burmister MLET theory to calculate the response of flexible pavement structures. In the development of the program, the time-consuming part of MLET processes was optimised. To improve the convergence and accuracy of responses in the vicinity of the surface of the top layer, an approach based on Richardsons extrapolation was employed. Moreover, an iterative approach to model stress dependency of unbound granular materials was incorporated. A comprehensive comparison of the program with two frequently used programs demonstrated an excellent agreement and improved performance.

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

Numerical Modelling of Thin Pavements Behaviour in Accelerated HVS Tests

ABSTRACT Two thin road structures have been tested in accelerated testing by using a Heavy Vehicle Simulator (HVS). Both were surface dressed structures, one with a target 20 cm thick unbound base course layer and the other with the base divided into a 10 cm bitumen stabilized base over 10 cm unbound base. The tested road structures were instrumented to estimate deflections, strains and stresses in various locations inside the structure. Numerical analyses, by using two different techniques, the multilayer elastic theory (MLET) and the finite element (FE) have been carried out to simulate the response behaviour of the tested structure and compared with the actual measurements. For both techniques linear and nonlinear behaviour of the base was assumed. For the FE method both 2D axisymmetric and a 3D analysis were carried out. The results have further been used to model the permanent deformation development in each layer. The main finding of the study was that induced vertical stresses were generally well predicted in both structures. Better agreement was generally found between the vertical stresses and the actual response with the non-linear response, especially for high loading conditions. The best prediction of surface deflections was obtained in a three dimensional linear elastic analysis where a rectangular loading area was used instead of a circular one in the two dimensional axisymmetric solutions. Generally, poor or moderate agreement was found between the strain measurements and the numerical estimations. The simple work hardening model used to model the accumulated deformation relied on results from repeated load triaxial test results and gave generally good agreement with the results from the testing.

On Forecasting the Resilient Modulus from the CBR Value of Granular Bases

ABSTRACT The unbound granular materials (UGM), base and subbase layers, play an essential role in the overall structural performance of thin pavement structures. They show complex stress dependent elasto-plastic behaviour under external loading. Therefore the UGM are commonly tested using the Repeated Load Triaxial (RLT) testing method to estimate the stiffness of the material by applying haversine loading pulses. The RLT testing method represents the actual stress situation quite adequately and gives satisfactorily estimates of the stiffness characteristics of UGM. A simple test that has been used for a long time in structural design of flexible pavements is the CBR (California Bearing Ratio) test. In the CBR test, the load-deformation curve is acquired while a plunger is penetrated into the material at a constant rate. In the literature one can find a number of relationships for UGM where the CBR value is used to predict the stiffness. These connections usually do not take into account that stiffness of UGM is both stress and moisture dependent. To investigate if a relationship between the two tests exists, twenty materials have been tested with both methods and the test results compared. The materials were of varying quality and were tested at four different moisture contents. The results indicate that a simple power law can be used to forecast the stiffness if the CBR-value is known.