Electronic structures of GaAs/AlxGa1-xAs quantum double

In the framework of effective mass envelope function theory, the electronic structures of GaAs/AlxGa1-xAs quantum double rings(QDRs) are studied. Our model can be used to calculate the electronic structures of quantum wells, wires, dots, and the single ring. In calculations, the effects due to the different effective masses of electrons and holes in GaAs and AlxGa1-xAs and the valence band mixing are considered. The energy levels of electrons and holes are calculated for different shapes of QDRs. The calculated results are useful in designing and fabricating the interrelated photoelectric devices. The single electron states presented here are useful for the study of the electron correlations and the effects of magnetic fields in QDRs.

Self-assembled GaAs quantum rings by MBE droplet epitaxy

Fabrication of semiconductor nanostructures such as quantum dots (QDs), quantum rings (QRs) has been considered as the important step for realization of solid state quantum information devices, including QDs single photon emission source, QRs single electron memory unit, etc. To fabricate GaAs quantum rings, we use Molecular Beam Epitaxy (MBE) droplet technique in this report. In this droplet technique, Gallium (Ga) molecular beams are supplied initially without Arsenic (As) ambience, forming droplet-like nano-clusters of Ga atoms on the substrate, then the Arsenic beams are supplied to crystallize the Ga droplets into GaAs crystals. Because the morphologies and dimensions of the GaAs crystal are governed by the interplay between the surface migration of Ga and As adatoms and their crystallization, the shape of the GaAs crystals can be modified into rings, and the size and density can be controlled by varying the growth temperatures and As/Ga flux beam equivalent pressures(BEPs). It has been shown by Atomic force microscope (AFM) measurements that GaAs single rings, concentric double rings and coupled double rings are grown successfully at typical growth temperatures of 200 C to 300 C under As flux (BEP) of about 1.0 x 10(-6) Torr. The diameter of GaAs rings is about 30-50 nm and thickness several nm.

Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Complex quantum ring structures formed by droplet epitaxy

Well-defined complex quantum ring structures formed by droplet epitaxy are demonstrated. By varying the temperature of the crystallizing Ga droplets and changing the As flux, GaAs/AlGaAs quantum single rings and concentric quantum double rings are fabricated, and double-ring complexes are observed. The growth mechanism of these quantum ring complexes is addressed. (c) 2006 American Institute of Physics.

Quantum interference effect in GaAs/AlGaAs double quantum wells

Quantum interference properties of GaAs/AlGaAs symmetric double quantum wells were investigated in a magnetic field parallel to heterointerfaces at 1.9 K. For two types of samples used in our experiments, two GaAs quantum wells with the same width of 60 Angstrom are separated by an AlGaAs barrier layer of 120 Angstrom and 20 degrees thick, respectively. The channels with the length of 2 mu m are defined by alloyed ohmic contacts. The conductance oscillation as a function of the magnetic flux Phi(= B/s) was observed and oscillation period is approximately equal to h/e. The results are in agreement with the theoretical expectation of the Aharonov-Bohm effect. Conductance oscillations are apparent slightly in the samples with a thinner AlGaAs barrier.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

黄土丘陵区不同土地利用方式下土壤水分入渗的对比试验

为更好地掌握黄土丘陵区不同土地利用方式下的土壤水分入渗性能,采用双环法和人工降雨法,分别对陕西省延安市燕沟流域林地、草地、农地3种土地利用方式的土壤水分入渗过程进行了对比试验。结果表明:双环法能较好的反映水向土中的入渗过程;而人工降雨法可以较为真实地反映天然降雨过程中雨水向土中的入渗过程, 两者有很大的不同,主要表现在土壤水分的入渗速率变化过程方面。前者测定的土壤水分入渗速率主要受制于土壤的物理性状,而后者:不但与土壤物理性状有关,还与降雨强度有较密切的关系。在人工模拟短历时暴雨条件下, 对于林地和荒坡草地,土壤水分入渗速率有随雨强增大而增大的趋势,而对于裸耕农地,随着雨强的增大,土壤水分入渗速率有降低的趋势。

Algebraische Beschreibung von Symmetrien: das Modell der Nichtkommutativen Multi-Tori

In der Nichtkommutativen Geometrie werden Räume und Strukturen durch Algebren beschrieben. Insbesondere werden hierbei klassische Symmetrien durch Hopf-Algebren und Quantengruppen ausgedrückt bzw. verallgemeinert. Wir zeigen in dieser Arbeit, daß der bekannte Quantendoppeltorus, der die Summe aus einem kommutativen und einem nichtkommutativen 2-Torus ist, nur den Spezialfall einer allgemeineren Konstruktion darstellt, die der Summe aus einem kommutativen und mehreren nichtkommutativen n-Tori eine Hopf-Algebren-Struktur zuordnet. Diese Konstruktion führt zur Definition der Nichtkommutativen Multi-Tori. Die Duale dieser Multi-Tori ist eine Kreuzproduktalgebra, die als Quantisierung von Gruppenorbits interpretiert werden kann. Für den Fall von Wurzeln der Eins erhält man wichtige Klassen von endlich-dimensionalen Kac-Algebren, insbesondere die 8-dim. Kac-Paljutkin-Algebra. Ebenfalls für Wurzeln der Eins kann man die Nichtkommutativen Multi-Tori als Hopf-Galois-Erweiterungen des kommutativen Torus interpretieren, wobei die Rolle der typischen Faser von einer endlich-dimensionalen Hopf-Algebra gespielt wird. Der Nichtkommutative 2-Torus besitzt bekanntlich eine u(1)xu(1)-Symmetrie. Wir zeigen, daß er eine größere Quantengruppen-Symmetrie besitzt, die allerdings nicht auf die Spektralen Tripel des Nichtkommutativen Torus fortgesetzt werden kann.

[Historical review and future orientations of the conventional vascular microanastomoses]

Microvascular surgery has become an important method for reconstructing surgical defects due to trauma, tumors or after burn. The most important factor for successful free flap transfer is a well-executed anastomosis. The time needed to perform the anastomosis and the failure rate are not negligible despite the high level of operator's experience. During the history, many alternatives were tried to help the microsurgeon and to reduce the complications. A Medline literature search was performed to find articles dealing with non-suture methods of microvascular anastomosis. Many historical books were also included. The non-suture techniques can be divided into four groups based on the used mechanism of sutures: double intubation including tubes and stents, intubation-eversion including simple rings, double eversion including staples and double rings, and wall adjustement with adhesives or laser. All these techniques were able to produce a faster and easier microvascular anastomosis. Nevertheless, disadvantages of the suturless techniques include toxicity, high cost, leakage or aneurysm formation. More refinement is needed before their widespread adoption. Thus, laser-assisted microvascular anastomosis using 1,9 μm diode laser appeared to be a safe and reliable help for the microsurgeon and may be further developed in the near future.

Generalized cluster states based on finite groups

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.

Constructing topological models by symmetrization: A projected entangled pair states study

Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group G˜ which is always non-Abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wave functions in the same phase as the double model of G˜. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of G˜.

Electronic structure of few-electron concentric double quantum rings

The ground state structure of few-electron concentric double quantum rings is investigated within the local spin density approximation. Signatures of inter-ring coupling in the addition energy spectrum are identified and discussed. We show that the electronic configurations in these structures can be greatly modulated by the inter-ring distance: At short and long distances the low-lying electron states localize in the inner and outer rings, respectively, and the energy structure is essentially that of an isolated single quantum ring. However, at intermediate distances the electron states localized in the inner and the outer ring become quasidegenerate and a rather entangled, strongly-correlated system is formed.

Vertically coupled double quantum rings at zero magnetic field

Within local-spin-density functional theory, we have investigated the ¿dissociation¿ of few-electron circular vertical semiconductor double quantum ring artificial molecules at zero magnetic field as a function of interring distance. In a first step, the molecules are constituted by two identical quantum rings. When the rings are quantum mechanically strongly coupled, the electronic states are substantially delocalized, and the addition energy spectra of the artificial molecule resemble those of a single quantum ring in the few-electron limit. When the rings are quantum mechanically weakly coupled, the electronic states in the molecule are substantially localized in one ring or the other, although the rings can be electrostatically coupled. The effect of a slight mismatch introduced in the molecules from nominally identical quantum wells, or from changes in the inner radius of the constituent rings, induces localization by offsetting the energy levels in the quantum rings. This plays a crucial role in the appearance of the addition spectra as a function of coupling strength particularly in the weak coupling limit.