Non-adiabatic Current Excitation in Quantum Rings

We investigate the difference in the response of a one-dimensional semiconductor quantum ring and a finite-width ring to a strong and short-lived time-dependent perturbation in the THz regime. In both cases the persistent current is modified through a nonadiabatic change of the many-electron states of the system, but by different mechanisms in each case.Comment: LaTeX, 5 pages with 6 embedded postscript figures, submitted to 20th Nordic Semiconductor Meeting, Tampere (2003

Magnetotransport in a double quantum wire: Modeling using a scattering formalism built on the Lippmann-Schwinger equation

We model electronic transport through a double quantum wire in an external homogeneous perpendicular magnetic field using a scattering formalism built on the Lippmann-Schwinger equation. In the scattering region a window is opened between the parallel wires allowing for inter- and intra-wire scattering processes. Due to the parity breaking of the magnetic field the ensuing subband energy spectrum of the double wire system with its regimes of hole- and electron-like propagating modes leads to a more structure rich conductance as a function of the energy of the incoming waves than is seen in a single parabolically confined quantum wire. The more complex structure of the evanescent modes of the system also leaves its marks on the conductance.Comment: RevTeX, 8 pages with 10 included postscript figures, high resolution version available at http://hartree.raunvis.hi.is/~vidar/Rann/DW_VGCST_06.pd

Influence of shape of quantum dots on their far-infrared absorption

We investigate the effects of the shape of quantum dots on their far-infrared absorption in an external magnetic field by a model calculation. We focus our attention on dots with a parabolic confinement potential deviating from the common circular symmetry, and dots having circular doughnut shape. For a confinement where the generalized Kohn theorem does not hold we are able to interprete the results in terms of a mixture of a center-of-mass mode and collective modes reflecting an excitation of relative motion of the electrons. The calculations are performed within the time-dependent Hartree approximation and the results are compared to available experimental results.Comment: RevTeX, 16 pages with 10 postscript figures included. Submitted to Phys. Rev.

Spin effects in a confined 2DEG: Enhancement of the g-factor, spin-inversion states and their far-infrared absorption

We investigate several spin-related phenomena in a confined two-dimensional electron gas (2DEG) using the Hartree-Fock approximation for the mutual Coulomb interaction of the electrons. The exchange term of the interaction causes a large splitting of the spin levels whenever the chemical potential lies within a Landau band (LB). This splitting can be reinterpreted as an enhancement of an effective g-factor, g*. The increase of g* when a LB is half filled can be accompanied by a spontaneous formation of a static spin-inversion state (SIS) whose details depend on the system sision state (SIS) whose details depend on the system size. The coupling of the states of higher LB's into the lowest band by the Coulomb interaction of the 2DEG is essential for the SIS to occur. The far-infrared absorption of the system, relatively insensitive to the spin splitting, develops clear signs of the SIS.Comment: 7 figure

Energy Injection Episodes in Gamma Ray Bursts: The Light Curves and Polarization Properties of GRB 021004

Several GRB afterglow light curves deviate strongly from the power law decay observed in most bursts. We show that these variations can be accounted for by including refreshed shocks in the standard fireball model previously used to interpret the overall afterglow behavior. As an example we consider GRB 021004 that exhibited strong light curve variations and has a reasonably well time-resolved polarimetry. We show that the light curves in the R-band, X-rays and in the radio can be accounted for by four energy injection episodes in addition to the initial event. The polarization variations are shown to be a consequence of the injections.Comment: 4 pages, 2 figures. To appear in ApJ

Local stresses, dyke arrest and surface deformation in volcanic edificesand rift zones

Field studies indicate that nearly all eruptions in volcanic edifices and rift zones are supplied with magma through fractures (dykes) that are opened by magmatic overpressure. While (inferred) dyke injections are frequent during unrest periods, volcanic eruptions are, in comparison, infrequent, suggesting that most dykes become arrested at certain depths in the crust, in agreement with field studies. The frequency of dyke arrest can be partly explained by the numerical models presented here which indicate that volcanic edifices and rift zones consisting of rocks of contrasting mechanical properties, such as soft pyroclastic layers and stiff lava flows, commonly develop local stress fields that encourage dyke arrest. During unrest, surface deformation studies are routinely used to infer the geometries of arrested dykes, and some models (using homogeneous, isotropic half-spaces) infer large grabens to be induced by such dykes. Our results, however, show that the dyke-tip tensile stresses are normally much greater than the induced surface stresses, making it difficult to explain how a dyke can induce surface stresses in excess of the tensile (or shear) strength while the same strength is not exceeded at the (arrested) dyke tip. Also, arrested dyke tips in eroded or active rift zones are normally not associated with dyke-induced grabens or normal faults, and some dykes arrested within a few metres of the surface do not generate faults or grabens. The numerical models show that abrupt changes in Young's moduli(stiffnesses), layers with relatively high dyke-normal compressive stresses (stress barriers), and weak horizontal contacts may make the dyke-induced surface tensile stresses too small for significant fault or graben formation to occur in rift zones or volcanic edifices. Also, these small surface stresses may have no simple relation to the dyke geometry or the depth to its tip. Thus, for a layered crust with weak contacts, straightforward inversion of surface geodetic data may lead to unreliable geometries of arrested dykes in active rift zones and volcanic edifices

Magnetization of noncircular quantum dots

We calculate the magnetization of quantum dots deviating from circular symmetry for noninteracting electrons or electrons interacting according to the Hartree approximation. For few electrons the magnetization is found to depend on their number, and the shape of the dot. The magnetization is an ideal probe into the many-electron state of a quantum dot.Comment: 11 RevTeX pages with 6 included Postscript figure

Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming

We study the global asymptotic stability in probability of the zero solution of linear stochastic differential equations with constant coefficients. We develop a sum-of-squares program that verifies whether a parameterized candidate Lyapunov function is in fact a global Lyapunov function for such a system. Our class of candidate Lyapunov functions are naturally adapted to the problem. We consider functions of the form $V(\mathbf{x}) = ||\mathbf{x}||^p_Q = (\mathbf{x}^\top Q \mathbf{x})^{\frac{p}{2}}$, where the parameters are the positive definite matrix $Q$ and the number p > 0. We give several examples of our proposed method and show how it improves previous results