Decoherence induced by an ordered environment

This Letter deals with the time evolution of a qubit weakly coupled to a reservoir which has a symmetry broken state with long range order at finite temperatures. In particular, we model the ordered reservoir by a standard BCS superconductor with s-wave pairing. We study the reduced density matrix of a qubit using both the time-convolutionless and Nakajima-Zwanzig approximations. We study different kinds of couplings between the qubit and the superconducting bath. We find that ordering in the superconducting bath generically leads to an unfavorable non- Markovian faster-than-exponential decay of the qubit coherence. On the other hand, a coupling of the qubit to the non-ordered sector of the bath can result in a Markovian decoherence of the qubit with a drastic reduction of the decoherence rate. Since these behaviors are endemic to the ordered phase, qubits can serve as useful probes of continuous phase transitions in their environment. We also briefly discuss the validity of our main result, faster than exponential decay of the qubit coherences, for a qubit coupled to a generic ordered bath with a spontaneously broken continuous symmetry at finite temperatures.Comment: 6 pages, 3 figure

Iterative Connections and Abhyankar's Conjecture

This thesis contains two major parts. In the first part, I introduce a new theory of modules with iterative connection. This theory unifies the theory of modules with connection in characteristic zero as given by N. Katz and the theory of iterative differential modules in positive characteristic as given by B. H. Matzat und M. van der Put. The second part of this work is about the differential Abhyankar conjecture for iterative Picard-Vessiot extensions (IPV-extensions). This conjecture is concerned with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for connected groups for being realisable with given singular points

Der Deutsche Naturschutzring

Der Deutsche Naturschutzring (DNR) ist ein Dachverband mit einer außerordentlich großen Vielfalt an Mitgliedsorganisationen. Die Arbeit belegt, wie dem DNR die Überwindung seiner aufgrund von Interessensdivergenzen verursachten Funktionsunfähigkeit als Dachverband der Naturschutzverbände und die von seinen Mitgliedern verlangte Ausweitung des Serviceangebotes gelingt. In den ersten drei Jahrzehnten der DNR-Existenz fanden selbst erheblich vom Hauptzweck des DNR abweichende Interessen Berücksichtigung bei der politischen Willensbildung im Verband. Die sekundären Naturschutzverbände dominierten dank der früheren Beitrags- und Stimmenregelung deutlich gegenüber den primären Naturschutzverbänden und setzten ihre Positionen durch. Erst nach den erfolgreich durchgeführten Reformen im DNR in den 80er Jahren verloren sie ihre Vorrangstellung und waren nicht mehr in der Lage, abweichenden Interessen zur Agrar-, Jagd- und Atompolitik im DNR durchzusetzen

On hypergeometric systems of differential equations

This thesis is about the hypergeometric system of differential equations. Until now, fundamental solutions for this system are just known in dimension 2 and very special cases in higher dimension. In dimension 2 it is solvable with the hypergeometric function. Under some assumptions there exist characteristic constants for the system and in dimension 2 they can be represented by means of the Gamma function. In this work the solutions and constants of a hypergeometric system have been considered as power series in a newly introduced parameter. Furthermore, two sequences of functions have been introduced and analyzed and the coefficients of the power series have been expressed in terms of these functions

A Network-Centric Design for Relationship-based Security and Access Control - Overview of the Security Architecture of the Stanford Integrated Digital Libraries Project

this paper, we survey some of the basics of a new relationship-based rights management design that we have designed to deal with security and access control in heterogeneous, networked environments. Specifically, we describe the following two system components of this design