Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Philosophy as a Path to Happiness : Attainment of Happiness in Arabic Peripatetic and Ismaili Philosophy

The aim of the dissertation is to explore the idea of philosophy as a path to happiness in classical Arabic philosophy. The starting point is in comparison of two distinct currents between the 10th and early 11th centuries, Peripatetic philosophy, represented by al-Fārābī and Ibn Sīnā, and Ismaili philosophy represented by al-Kirmānī and the Brethren of Purity. They initially offer two contrasting views about philosophy in that the attitude of the Peripatetics is rationalistic and secular in spirit, whereas for the Ismailis philosophy represents the esoteric truth behind revelation. Still, they converge in their view that the ultimate purpose of philosophy lies in its ability to lead man towards happiness. Moreover, they share a common concept of happiness as a contemplative ideal of human perfection, which refers primarily to an otherworldly state of the soul s ascent to the spiritual world. For both the way to happiness consists of two parts: theory and practice. The practical part manifests itself in the idea of the purification of the rational soul from its bodily attachments in order for it to direct its attention fully to the contemplative life. Hence, there appears an ideal of philosophical life with the goal of relative detachment from the worldly life. The regulations of the religious law in this context appear as the primary means for the soul s purification, but for all but al-Kirmānī they are complemented by auxiliary philosophical practices. The ascent to happiness, however, takes place primarily through the acquisition of theoretical knowledge. The saving knowledge consists primarily of the conception of the hierarchy of physical and metaphysical reality, but all of philosophy forms a curriculum through which the soul gradually ascends towards a spiritual state of being along an order that is inverse to the Neoplatonic emanationist hierarchy of creation. For Ismaili philosophy the ascent takes place from the exoteric religious sciences towards the esoteric philosophical knowledge. For Peripatetic philosophers logic performs the function of an instrument enabling the ascent, mathematics is treated either as propaedeutic to philosophy or as a mediator between physical and metaphysical knowledge, whereas physics and metaphysics provide the core of knowledge necessary for the attainment of happiness.

The EU and Institutional Twinning in Morocco - An inquiry into the motives of cooperation through discourse ethics

This study examines Institutional Twinning in Morocco as a case of EU cooperation through the pragmatic, ethical and moral logics of reason in Jürgen Habermas’s discourse ethics. As a former accession tool, Twinning was introduced in 2004 for legal approximation in the context of the European Neighborhood Policy. Twinning is a unique instrument in development cooperation from a legal perspective. With its long historical and cultural ties to Europe, Morocco presents an interesting case study of this new form of cooperation. We will analyse motives behind the Twinning projects on illegal immigration, environment legislation and customs reform. As Twinning is a new policy instrument within the ENP context, there is relatively little preceding research, which, in itself, constitutes a reason to inquire into the subject. While introducing useful categories, the approaches discussing “normative power Europe” do not offer methodological tools precise enough to analyse the motives of the Twinning cooperation from a broad ethical standpoint. Helene Sjursen as well as Esther Barbé and Elisabeth Johansson-Nogués have elaborated on Jürgen Habermas’ discourse ethics in determining the extent of altruism in the ENP in general. Situating the analysis in the process-oriented framework of Critical Theory, discourse ethics provides the methodological framework for our research. The case studies reveal that the context in which they operate affects the pragmatic, ethical and moral aspirations of the actors. The utilitarian notion of profit maximization is quite pronounced both in terms of the number of Twinning projects in the economic sphere and the pragmatic logics of reason instrumental to security and trade-related issues. The historical background as well internal processes, however, contribute to defining areas of mutual interest to the actors as well as the motives Morocco and the EU sometimes described as the external projection of internal values. Through its different aspects, Twinning cooperation portrays the functioning of the pragmatic, ethical and moral logics of reason in international relations.