Lectures on conformal field theory and Kac-Moody algebras

This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate Course on Conformal Field Theory and Integrable Models (Budapest, August 1996), to appear in Springer Lecture Notes in Physic

Precision cutting of glassy polymers: influence of aging on the cutting process

ABSTRACT This paper presents the results of an experimental study on the influence of aging on the cutting mechanics of glassy polymers. Polystyrene (PS), a glassy polymer, typically behaves brittle when subjected to a stress, it can be made ductile by rejuvenation. It was expected that PS would show a different cutting behaviour when it would be aged or rejuvenated. To investigate this two different molecular weight PS grades were used. Both aged and (mechanically) rejuvenated samples were made from each grade and cut. Cutting forces, chip morphology and surface quality were investigated. Although the chips showed no differences in brittleness and ductility, the measured cutting forces indicated that there is a difference between aged and rejuvenated PS. Also an interesting difference in cutting forces between the two PS grades was found. Investigation of the surface quality of the PS samples showed that the aged samples have smoother surfaces than the rejuvenated samples. It can be concluded that aging does have effect on the cutting mechanics and the obtained surface roughness

Preferential degradation of polyphenols from Sphagnum - 4-isopropenylphenol as a proxy for past hydrological conditions in Sphagnum-dominated peat

The net accumulation of remains of Sphagnum spp. is fundamental to the development of many peatlands. The effect of polyphenols from Sphagnum on decomposition processes is frequently cited but has barely been studied. The central area of the Rödmossamyran peatland (Sweden) is an open lawn that consists mostly of Sphagnum spp. with a very low contribution from vascular plants. In order to determine the effects of decay on sphagnum phenols, 53 samples of a 2.7 m deep core from this lawn were analysed with pyrolysis gas chromatography-mass spectrometry (pyrolysis-GC/MS) and compared with more traditional decomposition proxies such as C/N ratio, UV light transmission of alkaline peat extracts, and bulk density. Factor Analysis of 72 quantified pyrolysis products suggested that the variation in 4-isopropenylphenol was largely determined by aerobic decomposition instead of Sphagnum abundance. In order to evaluate the effects of aerobic decay in Sphagnum peat, down-core records from different climatic regions were compared using molecular markers for plant biopolymers and C/N ratio. These included markers for lignin from vascular plants ((di)methoxyphenols), polyphenols from Sphagnum spp. (4-isopropenylphenol), and cellulose (levoglucosan). Our results indicate that polyphenols from Sphagnum are preferentially degraded over polysaccharides; consequently the variability of the marker for sphagnum acid, 4-isopropenylphenol, was found indicative of decomposition instead of reflecting the abundance of Sphagnum remains. The fact that 4-isopropenylphenol is aerobically degraded in combination with its specificity for Sphagnum spp. makes it a consistent indicator of past hydrological conditions in Sphagnum-dominated peat. In contrast, the variability of C/N records in Sphagnum-dominated peat was influenced by both vegetation shifts and decomposition, and the dominant effect differed between the studied peatlands. Our results provide direction for modelling studies that try to predict possible feedback mechanisms between peatlands and future climate change, and indicate that the focus in Sphagnum decay studies should be on carbohydrates rather than on phenolic compounds

Quantum many-body simulations using Gaussian phase-space representations

Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the early work of Wigner, Glauber and Sudarshan. We focus on modern phase-space approaches using non-classical phase-space representations. These lead to the Gaussian representation, which unifies bosonic and fermionic phase-space. Examples treated include quantum solitons in optical fibers, colliding Bose-Einstein condensates, and strongly correlated fermions on lattices.Comment: Short Review (10 pages); Corrected typo in eq (14); Added a few more reference

Aspects of Fractional Superstrings

We investigate some issues relating to recently proposed fractional superstring theories with $D_{\rm critical}<10$. Using the factorization approach of Gepner and Qiu, we systematically rederive the partition functions of the $K=4,\, 8,$ and $16$ theories and examine their spacetime supersymmetry. Generalized GSO projection operators for the $K=4$ model are found. Uniqueness of the twist field, $\phi^{K/4}_{K/4}$, as source of spacetime fermions is demonstrated. Last, we derive a linear (rather than quadratic) relationship between the required conformal anomaly and the conformal dimension of the supercurrent ghost.Comment: 36 pages, CALT-68-1756 Revisions to match form to appear in Comm. Math. Phys. Use standard TeX. Derivation of affine partition functions related to $D=4,6$ models is now shown. References Update

Theory for a Hanbury Brown Twiss experiment with a ballistically expanding cloud of cold atoms

We have studied one-body and two-body correlation functions in a ballistically expanding, non-interacting atomic cloud in the presence of gravity. We find that the correlation functions are equivalent to those at thermal equilibrium in the trap with an appropriate rescaling of the coordinates. We derive simple expressions for the correlation lengths and give some physical interpretations. Finally a simple model to take into account finite detector resolution is discussed

Design of a five-axis ultra-precision micro-milling machine—UltraMill. Part 1: Holistic design approach, design considerations and specifications

High-accuracy three-dimensional miniature components and microstructures are increasingly in demand in the sector of electro-optics, automotive, biotechnology, aerospace and information-technology industries. A rational approach to mechanical micro machining is to develop ultra-precision machines with small footprints. In part 1 of this two-part paper, the-state-of-the-art of ultra-precision machines with micro-machining capability is critically reviewed. The design considerations and specifications of a five-axis ultra-precision micro-milling machine—UltraMill—are discussed. Three prioritised design issues: motion accuracy, dynamic stiffness and thermal stability, formulate the holistic design approach for UltraMill. This approach has been applied to the development of key machine components and their integration so as to achieve high accuracy and nanometer surface finish

Can a Lattice String Have a Vanishing Cosmological Constant?

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.Comment: 14 page

An Effective Superstring Spectral Action

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma model and derive an expression for the generalized loop space Dirac operator, in presence of a general background, using canonical quantization. The spectral action principle is used to show that the superstring partition function is also a spectral action valid for the fluctuations of the string modes.Comment: 31 pages, Latex fil

Quantum dynamics in ultra-cold atomic physics

We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially large. These phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum EPR entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorp- tion, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator