Representation Theoretical Construction of the Classical Limit and Spectral Statistics of Generic Hamiltonian Operators

Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction in chapter 1 this problem is motivated by a general construction of the classical limit for quantum mechanical systems, which is adopted to this setting, in chapter 2. In chapter 3 it is shown that for simple operators, i.e., operators of the Lie algebra the nearest neighbor statistics along a sequence of irreducible representations converge to the Dirac measure. After a suitable completion of the universal enveloping algebra the convergence to Poisson statistics is proved in chapter 4 for the exponentials of generic operators. The proof makes use of a combinatorial inequality of the Katz-Sarnak type for tori, which is proved in chapter 5. In the appendix the necessary facts from group theory and the theory of nearest neighbor distributions are gathered.Comment: 80 pages, 5 figures, phd thesis of the autho

TCNQ salts of planar metal complex cations: novel molecular conductors and semiconductors

The facile variation of positive charge of oxamide oxime metal complexes, caused by acid-base equilibrium, allows the growth of single crystals of their TCNQ salts. 1:1 salts consist of reqular segregated stacks of the components, with metallic room temperature behaviour of the Ni compound, the Pt compound being a semiconductor. Room temperature conductivities are of the order of 10 Siemens per cm. A 2:3 Pt complex TCNQ salt contains segregated acceptor stacks with half a negative charge per molecule. These stacks run perpendicular to mixed stacks -D-D-A-D-D-A-, with integral charges on donors D and acceptors A

A novel molecular metal: (oxamide oximato)(oxamide oxime)nickel(II) tetracyanoquinodimethanide, [Ni(oaoH)(oaoH2)]tcnq, and physical properties of its semiconducting Pt analogue

(C4H11N8NiO4)+(C12H4N4)-, Mr = 498.09 is triclinic, p1, a -=3.7718(6), b = 7.436(2), c =17.511(4) A, a=88.67(2), β=86.93(2), γ=85.05(2), γ= 488.51 A 3, Z = 1, d c=1.69 gcm -3, final R w= 0.035 for 1454 observed independent reflections. The crystals consist of segregated regular parallel stacks of planar metal complex cations and tcnq - counterions with intermolecular H bonds stabilizing the structure. The compound is metallic at room temperature. A metal to semiconductor transition around 230 K shows up in thermopower data, in the microwave conductivity and epr around 170 K. It is not visible in the static magnetic susceptibility

Spotlights Lehre. Transferpaket zur Verzahnung und Vernetzung von Fachwissenschaft und Fachdidaktik.

Die vorliegende Publikation versteht sich als Ideengeber für die universitäre Lehre in der Lehrerbildung in Gestalt eines sogenannten Transferpakets. Sie berichtet über Ergebnisse des Teilprojekts ‚Spotlights-Lehre‘ des Projekts ‚Schnittstellen gestalten – Lehrerbildung entlang des Leitbildes des "Reflective Practitioner" an der Universität Bremen' im BMBF-Programm ‚Qualitätsoffensive Lehrerbildung‘. Inhaltlich geht es um innovative Lehrprojekte zur Verzahnung und Vernetzung von Fachwissenschaft und Fachdidaktik, die das Ziel verfolgen, Fragmentierungserfahrungen von Lehramtsstudierenden in den Fächern Mathematik, Englisch, Romanistik, Geschichte und Inklusive Didaktik zu reduzieren. Zentrales Anliegen dieses Transferpakets ist es, Transferstrategien bereitzustellen, an Beispielen zu illustrieren und in Lehrbeschreibungen einzubetten. Umfassend wird gezeigt, wie die Designprozesse zur Lehre in den beiden zentralen Modellprojekten der Fächer Englisch und Mathematik gestaltet sowie die Transfer- und Vernetzungsstrategien gewonnen wurden

Darstellungstheoretische Konstruktion des klassischen Grenzfalls und Spektralstatistik generischer Hamiltonoperatoren

Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed.After a short introduction in chapter 1 this problem is motivated by a general construction of the classical limit for quantum mechanical systems, which is adopted to this setting, in chapter 2. In chapter 3 it is shown that for simple operators, i.e., operator of the Lie algebra the nearest neighbor statistics along a sequence of irreducible representations converge to the Dirac measure. After a suitable completion of the universal enveloping algebra the convergence to Poisson statistics is proved in chapter 4 for the exponentials of generic operators. The proof makes use of a combinatorial inequality of the Katz-Sarnak type for tori, which is proved in chapter 5. In the appendix the necessary facts from group theory and the theory of nearest neighbor distributions are gathered