Spin-polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena

Mesoscopic conductors are electronic systems of sizes in between nano- and micrometers, and often of reduced dimensionality. In the phase-coherent regime at low temperatures, the conductance of these devices is governed by quantum interference effects, such as the Aharonov-Bohm effect and conductance fluctuations as prominent examples. While first measurements of quantum charge transport date back to the 1980s, spin phenomena in mesoscopic transport have moved only recently into the focus of attention, as one branch of the field of spintronics. The interplay between quantum coherence with confinement-, disorder- or interaction-effects gives rise to a variety of unexpected spin phenomena in mesoscopic conductors and allows moreover to control and engineer the spin of the charge carriers: spin interference is often the basis for spin-valves, -filters, -switches or -pumps. Their underlying mechanisms may gain relevance on the way to possible future semiconductor-based spin devices. A quantitative theoretical understanding of spin-dependent mesoscopic transport calls for developing efficient and flexible numerical algorithms, including matrix-reordering techniques within Green function approaches, which we will explain, review and employ.Comment: To appear in the Encyclopedia of Complexity and System Scienc

Galois extensions of Lubin-Tate spectra

Let E_n be the n-th Lubin-Tate spectrum at a prime p. There is a commutative S-algebra E^{nr}_n whose coefficients are built from the coefficients of E_n and contain all roots of unity whose order is not divisible by p. For odd primes p we show that E^{nr}_n does not have any non-trivial connected finite Galois extensions and is thus separably closed in the sense of Rognes. At the prime 2 we prove that there are no non-trivial connected Galois extensions of E^{nr}_n with Galois group a finite group G with cyclic quotient. Our results carry over to the K(n)-local context.Comment: revised version in final for

Scope and semimodal verbs: two approaches

In this paper I focus on scope phenomena connected with semimodal (and modal) verbs and mainly on the syntactic behaviour of these groups of verbs. One important question is: why can semimodal verbs (and modal verbs in epistemic use) not have perfect and future tense forms? Taking among other things Reichenbach's tense system as a starting point I try to point out that the interpretation of a semimodal or a modal in epistemic use is problematic 1. if there is more than one reference time/if the reference time is indefinite or 2. if the verb in question stands together with an auxiliary of future which has a certain modal meaning itself. The comparison of the treatment of these phenomena in the framework of the Semantic Syntax with a non transformational approach (fragment of a categorial grammar) shows, that some important transformational rules and principles easily and economically can be represented in a non transformational grammar. The transformational approach needs rules like RAISING and LOWERING (or at least one of the two, and in addition to this a rather extended set of rules) for the generation of sentences, while in the categorial system we need only two reduction laws. It has to be investigated whether and to what extent the formation and transformation rules in a transformational grammar on the one hand and the dominance / linear precedence rules together with the lexical entries on the other hand are equivalent

Weak products of complete Pick spaces

Let $\mathcal H$ be the Drury-Arveson or Dirichlet space of the unit ball of $\mathbb C^d$. The weak product $\mathcal H\odot\mathcal H$ of $\mathcal H$ is the collection of all functions $h$ that can be written as $h=\sum_{n=1}^\infty f_n g_n$, where $\sum_{n=1}^\infty \|f_n\|\|g_n\|<\infty$. We show that $\mathcal H\odot\mathcal H$ is contained in the Smirnov class of $\mathcal H$, i.e. every function in $\mathcal H\odot\mathcal H$ is a quotient of two multipliers of $\mathcal H$, where the function in the denominator can be chosen to be cyclic in $\mathcal H$. As a consequence we show that the map $\mathcal N \to clos_{\mathcal H\odot\mathcal H} \mathcal N$ establishes a 1-1 and onto correspondence between the multiplier invariant subspaces of $\mathcal H$ and of $\mathcal H\odot\mathcal H$. The results hold for many weighted Besov spaces $\mathcal H$ in the unit ball of $\mathbb C^d$ provided the reproducing kernel has the complete Pick property. One of our main technical lemmas states that for weighted Besov spaces $\mathcal H$ that satisfy what we call the multiplier inclusion condition any bounded column multiplication operator $\mathcal H \to \oplus_{n=1}^\infty \mathcal H$ induces a bounded row multiplication operator $\oplus_{n=1}^\infty \mathcal H \to \mathcal H$. For the Drury-Arveson space $H^2_d$ this leads to an alternate proof of the characterization of interpolating sequences in terms of weak separation and Carleson measure conditions.Comment: minor change

Ideen zur Veranschaulichung von Aussagen mit Modalverben Sprachwissenschaftliche Annahmen - für den Unterricht aufbereitet

The topic of the present paper is the relation between linguistics and language education. Put as a question one could ask: 'what benefit can linguistics have for language teaching?'. It will be claimed that as a precondition, language teachers should have more than just marginal insight into theories of natural language. I will try to support this postulate using sentences with modal verbs: based on a certain linguistic theory, illustrations of sentences with modal verbs will be given. These illustrations are thought to be a first step for a didactic preparation (transformation) of explanations given by a linguistic theory for natural language phenomena. As a consequence of the considerations it will be postulated that it is obligatory for the education of teachers to include linguistic modules, since, in line with the hypothesis of this paper, insight into linguistic theories can help: 1) to understand phenomena of natural language and 2) to find a didactical preparation for the phenomena in question