Form Factors for Quasi-particles in c=1 Conformal Field Theory

The non-Fermi liquid physics at the edge of fractional quantum Hall systems is described by specific chiral Conformal Field Theories with central charge c=1. The charged quasi-particles in these theories have fractional charge and obey a form of fractional statistics. In this paper we study form factors, which are matrix elements of physical (conformal) operators, evaluated in a quasi-particle basis that is organized according to the rules of fractional exclusion statistics. Using the systematics of Jack polynomials, we derive selection rules for a special class of form factors. We argue that finite temperature Green's functions can be evaluated via systematic form factor expansions, using form factors such as those computed in this paper and thermodynamic distribution functions for fractional exclusion statistics. We present a specific case study where we demonstrate that the form factor expansion shows a rapid convergence.Comment: 36 pages, 1 postscript figur

Quasi-particles for quantum Hall edges

We discuss a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. Fundamental quasi-particles for the Laughlin state with filling fraction \nu =1/3 are edge electrons of charge -e and edge quasi-holes of charge +e/3. These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a kinetic equation for charge transport between a \nu=1/3 fractional quantum Hall edge and a normal metal.Comment: Latex, 6 pages, Contribution to the proceedings of the XXXIVth Rencontres de Moriond `Quantum Physics at Mesoscopic Scale

1,4-diacetoxy-β-lactams. Reactions with nucleophiles

β-Lactam reacts with hetero nucleophiles under ring cleavage to give 2,2-dimethyl-3-oximinobutanoic esters 6 and 7 . N-hydroxyazetidine 5 , the precursor of β-lactam 1, is prepared by a new method

Short and random: Modelling the effects of (proto-)neural elongations

To understand how neurons and nervous systems first evolved, we need an account of the origins of neural elongations: Why did neural elongations (axons and dendrites) first originate, such that they could become the central component of both neurons and nervous systems? Two contrasting conceptual accounts provide different answers to this question. Braitenberg's vehicles provide the iconic illustration of the dominant input-output (IO) view. Here the basic role of neural elongations is to connect sensors to effectors, both situated at different positions within the body. For this function, neural elongations are thought of as comparatively long and specific connections, which require an articulated body involving substantial developmental processes to build. Internal coordination (IC) models stress a different function for early nervous systems. Here the coordination of activity across extended parts of a multicellular body is held central, in particular for the contractions of (muscle) tissue. An IC perspective allows the hypothesis that the earliest proto-neural elongations could have been functional even when they were initially simple short and random connections, as long as they enhanced the patterning of contractile activity across a multicellular surface. The present computational study provides a proof of concept that such short and random neural elongations can play this role. While an excitable epithelium can generate basic forms of patterning for small body-configurations, adding elongations allows such patterning to scale up to larger bodies. This result supports a new, more gradual evolutionary route towards the origins of the very first full neurons and nervous systems.Comment: 12 pages, 5 figures, Keywords: early nervous systems, neural elongations, nervous system evolution, computational modelling, internal coordinatio