Abstract:
The classical drift motion of electrons in crossed electric and magnetic fields provides an interesting example of a system with an on average constant velocity -- despite the presence of an electric field. This drift-velocity depends solely on the ratio of the electric and magnetic fields and not on the initial momentum of the electron. The present work describes the quantum-mechanical version of this drift-motion, which differs drastically from the classical result: The drift becomes dependent on the energy and a quantization of the transport occurs. The results bear implications for the theory of the quantum Hall effect: Current theories neglect the electric Hall-field (which is perpendicular to a magnetic field) and thus do not include the quantization due to the crossed-field geometry. I will discuss why it is not possible to eliminate the electric field and how one can explain the quantization in crossed fields in a semiclassical picture. These results make it possible to construct an alternative theory of the quantum Hall effect.

Abstract:
Matter waves originating from a localized region in space appear commonly in physics. Examples are photo-electrons, ballistic electrons in nanotechnology devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released from a coherent source (atom laser). We introduce the energy-dependent Green function as a suitable tool to calculate the arising currents. For some systems experimental data is available and in excellent agreement with the presented results.

Abstract:
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane, which is commonly the case in nanodevices. We compare the exact solution with the semiclassical energy spectrum and study the time-dependent dynamics of the system using the time-dependent variational principle.

Abstract:
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized wave-packet reveals the eigenstates and eigenvalues of the system under consideration. We discuss applications of the wave-packet method in atomic, molecular, and mesoscopic systems and point out specific advantages of the time-dependent approach. In connection with the familiar initial value formulation of classical mechanics, an intuitive interpretation of transport emerges. For interacting many-particle systems, we discuss the efficient calculation of the self-consistent classical transport in the presence of a magnetic field.

Abstract:
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic fields is employed to construct a non-linear transport theory. Another important ingredient of the alternative theory is the coupling of the two-dimensional electron gas to the leads and the applied voltages. By working in a picture, where the external voltages fix the chemical potential in the 2D subsystem, the experimentally observed linear relation between the voltage and the location of the quantum Hall plateaus finds an natural explanation. Also, the classical Hall effect emerges as a natural limit of the quantum Hall effect. For low temperatures (or high currents), a non-integer substructure splits higher Landau levels into sublevels. The appearence of substructure and non-integer plateaus in the resistivity is NOT linked to electron-electron interactions, but caused by the presence of a (linear) electric field. Some of the resulting fractions correspond exactly to half-integer plateaus.

Abstract:
Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the quantum current through a Hall device that does not invoke disorder or interactions as the cause of the integer quantum Hall effect (QHE), but is based on a proper quantization of the classical electron drift motion. The theory yields a quantitative description of the breakdown of the QHE at high current densities that is in agreement with experimental data. Furthermore, several of its key points are in line with recent findings of experiments that address the dependency of the QHE on the 2DEG bias voltage, results that are not easily explained within the framework of conventional QHE models.

Abstract:
Solving the quantum-mechanical many-body problem requires scalable computational approaches, which are rooted in a good understanding of the physics of correlated electronic systems. Interacting electrons in a magnetic field display a huge variety of eigenstates with different internal structures, which have been probed experimentally in the Hall effect. The advent of high-performing graphics processing units has lead to a boost in computational speed in particular for classical systems. In the absence of a quantum-computer, it is thus of importance to see how quantum-mechanical problems can be cast into a seemingly classical dynamics, which can be efficiently implemented. At the same time, such mappings provide insights into the quantum-to-classical transition of many-body systems.

Abstract:
We present an extension of the spin-adapted configuration-interaction method for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and center-of-mass coordinates we obtain an analytical identification of all spurious center-of-mass states of the Coulomb-interacting electrons. We find a substantial reduction in the basis set used for numerical computations. At the same time we increase the accuracy compared to the standard spin-adapted configuration-interaction method (SACI) due to the absence of distortions caused by an unbalanced cut-off of center-of-mass excitations.

Abstract:
Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state boundary conditions are related in terms of transfer matrices. Scenarios of positive and negative energy are distinguished. The dependence on the potential strength parameter is analyzed. The scattering matrix is computed. Implications for the interpretation of band germs in quasiperiodic chains are discussed.

Abstract:
El tema de efectos transitorios en mecácanica cuántica ha sido de interés para uno de los autores (MM) desde hace mucho tiempo, cuando aún no había técnicas experimentales para observarlos. En particular, el problem ade abrir instantáneamente un obturador lo llevo al concepto de difracción en el tiempo [1]. Desde el punto de vista físico sólo se puede abrir un obturador como función del tiempo, y esto complica grandemente el problema ya que entonces no es invariante ante translaciones en el tiempo y por ello, entre otras dificultades, la energía del sistema no es una constante de movimiento. Kleber y Scheitler [2] analizaron el problema describiendo el obturador como un potencial ± en el origen x = 0, pero cuya intensidad es una función inversa del tiempo. En este trabajo seguimos otro procedimiento agregando a nuestro canal inicial de dos partículas otro nuevo, y los hacemos interactuar a través de apropiadas condiciones estacionarias a la frontera en el punto de coincidencia de los dos canales. El problema completo conserva la energía total, pero esto no sucede si nos restringimos sólo a la descripción en el primer canal. Por ello tenemos un modelo, (soluble analíticamente con ayuda de una transfomrada de Laplace) de algunos aspectos de un obturador que se abre como función del tiempo y lo comparamos con el análisis de la referencia [2].