Abstract:
We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by a Dirac-like Hamiltonian associated with a pseudospin one. The enlarged pseudospin S = 1 (instead of S = 1/2 as for graphene) leads to an enhanced "super" Klein tunneling through rectangular electrostatic barriers. Our results are confirmed via numerical investigation of the tight-binding model of the lattice. For a uniform magnetic field, we discuss the Landau levels and we investigate the transparency of a rectangular magnetic barrier. We show that the latter can mainly be described by semiclassical orbits bending the particle trajectories, qualitatively similar as it is the case for graphene. This makes it possible to confine particles with magnetic barriers of sufficient width.

Abstract:
In computerized adaptive testing (CAT) procedures within the framework of probabilistic test theory the difficulty of an item is adjusted to the ability of the respondent, with the aim of maximizing the amount of information generated per item, thereby also increasing test economy and test reasonableness.However, earlier research indicates that respondents might feel over-challenged by a constant success probability of p=0.5 and therefore cannot come to a sufficiently high answer certainty within a reasonable timeframe. Consequently response time per item increases, which – depending on the test material – can outweigh the benefit of administering optimally informative items. Instead of a benefit, the result of using CAT procedures could be a loss of test economy.Based on this problem, an adaptive success control algorithm was designed and tested, adapting the success probability to the working style of the respondent. Persons who need higher answer certainty in order to come to a decision are detected and receive a higher success probability, in order to minimize the test duration (not the number of items as in classical CAT). The method is validated on the re-analysis of data from the Adaptive Matrices Test (AMT, Hornke, Etzel & Rettig, 1999) and by the comparison between an AMT version using classical CAT and an experimental version using Adaptive Success Control.The results are discussed in the light of psychometric and psychological aspects of test quality.

Abstract:
The lowest eigenenergies of few, strongly interacting electrons in a one--dimensional ring are studied in the presence of an impurity barrier. The persistent current $\:I\:$, periodic in an Aharonov--Bohm flux penetrating the ring, is strongly influenced by the electron spin. The impurity does not remove discontinuities in $\:I\:$ at zero temperature. The total electron spin of the ground state oscillates with the flux. Strong electron--electron interaction enhances $\:I\:$, albeit not up to the value of the clean ring which itself is smaller than $\:I\:$ for free electrons. $\:I\:$ disappears on a temperature scale that depends exponentially on the electron density. In the limit of very strong interaction the response to small fluxes is diamagnetic.

Abstract:
Coherent Rashba spin precession along interacting multi-mode quantum channels is investigated, revisiting the theory of coupled Tomonaga-Luttinger liquids. We identify susceptibilities as the key-parameters to govern exponents and Rashba precession lengths. In semiconducting quantum wires spins of different transport channels are found to {\em dephase} in their respective precession angles with respect to one another, as a result of the interaction. This could explain the experimental difficulty to realize the Datta Das transistor. In single walled carbon nanotubes, on the other hand, interactions are predicted to suppress dephasing between the two flavor modes at small doping.

Abstract:
Dispersionless (flat) electronic bands are investigated regarding their conductance properties. Due to "caging" of carriers these bands are usually insulating at partial filling, at least on the non-interacting level. Considering the specific example of a $\mathcal{T}_3$--lattice we study long-range Coulomb interactions. A non-trivial dependence of the conductivity on flat band filling is obtained, exhibiting an infinite number of zeros. Near these zeros, the conductivity rises linearly with carrier density. At densities half way in between adjacent conductivity-zeros, strongly enhanced conductivity is predicted, accompanying a solid-solid phase transition.

Abstract:
Rashba precession of spins moving along a one-dimensional quantum channel is calculated, accounting for Coulomb interactions. The Tomonaga--Luttinger model is formulated in the presence of spin-orbit scattering and solved by Bosonization. Increasing interaction strength at decreasing carrier density is found to {\sl enhance} spin precession and the nominal Rashba parameter due to the decreasing spin velocity compared with the Fermi velocity. This result can elucidate the observed pronounced changes of the spin splitting on applied gate voltages which are estimated to influence the interface electric field in heterostructures only little.