Generalized Particle Statistics in Two-Dimensions: Examples from the Theory of Free Massive Dirac Field

In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group methods. The violation of Haag duality, the topological peculiarity of a two-dimensional space-time and the fact that unitary implementers do not lie in the global field algebra account for strange behaviour of statistics, which is no longer an intrinsic property of sectors. Since automorphisms are not inner, we exploit asymptotic abelianness of intertwiners in order to construct a braiding for a suitable $C^*$-tensor subcategory of End($\mathscr{A}$). We define two inequivalent classes of path connected bi-asymptopias, selecting only those sets of nets which yield a true generalized statistics operator.Comment: 24 page

A method for three-dimensional particle sizing in two-phase flows

A method is devised for true three-dimensional (3D) particle sizing in two-phase systems. Based on a ray-optics approximation of the Mie scattering theory for spherical particles, and under given assumptions, the principle is applicable to intensity data from scatterers within arbitrary interrogation volumes. It requires knowledge of the particle 3D location and intensity, and of the spatial distribution of the incident light intensity throughout the measurement volume. The new methodology is particularly suited for Lagrangian measurements: we demonstrate its use with the defocusing digital particle image velocimetry technique, a 3D measurement technique that provides the location, intensity and velocity of particles in large volume domains. We provide a method to characterize the volumetric distribution of the incident illumination and we assess experimentally the size measurement uncertainty

Branes: from free fields to general backgrounds

Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection coefficients for bulk fields on the disk; and second, a choice of an automorphism $\omega$ of the fusion rules that preserves conformal weights. Non-trivial automorphisms $\omega$ correspond to D-brane configurations for arbitrary conformal field theories. The choice of the fusion rule automorphism $\omega$ amounts to fixing the dimension and certain global topological features of the D-brane world volume and the background gauge field on it. We present evidence that for fixed choice of $\omega$ the boundary conditions are classified as the irreducible representations of some commutative associative algebra, a generalization of the fusion rule algebra. Each of these irreducible representations corresponds to a choice of the moduli for the world volume of the D-brane and the moduli of the flat connection on it.Comment: 56 pages, LaTeX2e. Typos corrected; two references adde

Fredholm determinants and the statistics of charge transport

Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certain operator in the one-particle Hilbert space. The formula is equivalent to a formula of Levitov and Lesovik in the finite dimensional case and may be viewed as its regularized form in general. Our result embodies two tenets often realized in mesoscopic physics, namely, that the transport properties are essentially independent of the length of the leads and of the depth of the Fermi sea.Comment: 30 pages, 2 figures, reference added, credit amende

Computational Inverse Problems

Inverse problem typically deal with the identification of unknown quantities from indirect measurements and appear in many areas in technology, medicine, biology, finance, and econometrics. The computational solution of such problems is a very active, interdisciplinary field with close connections to optimization, control theory, differential equations, asymptotic analysis, statistics, and probability. The focus of this workshop was on hybrid methods, model reduction, regularization in Banach spaces, and statistical approaches

Photoionization of few electron systems with a hybrid Coupled Channels approach

We present the hybrid anti-symmetrized coupled channels method for the calculation of fully differential photo-electron spectra of multi-electron atoms and small molecules interacting with strong laser fields. The method unites quantum chemical few-body electronic structure with strong-field dynamics by solving the time dependent Schr\"odinger equation in a fully anti-symmetrized basis composed of multi-electron states from quantum chemistry and a one-electron numerical basis. Photoelectron spectra are obtained via the time dependent surface flux (tSURFF) method. Performance and accuracy of the approach are demonstrated for spectra from the helium and berryllium atoms and the hydrogen molecule in linearly polarized laser fields at wavelength from 21 nm to 400 nm. At long wavelengths, helium and the hydrogen molecule at equilibrium inter-nuclear distance can be approximated as single channel systems whereas beryllium needs a multi-channel description

Uncertainty damping in kinetic traffic models by driver-assist controls

In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the vehicles, by which we prove that it is possible to dampen the propagation of such an uncertainty across the scales. Our analytical and numerical results suggest that the aggregate traffic flow may be made more ordered, hence predictable, by implementing such control protocols in driver-assist vehicles. Remarkably, they also provide a precise relationship between a measure of the macroscopic damping of the uncertainty and the penetration rate of the driver-assist technology in the traffic stream

Efficient Thermodynamic Description of Multi-Component One-Dimensional Bose Gases

We present a new method of obtaining nonlinear integral equations characterizing the thermodynamics of one-dimensional multi-component gases interacting via a delta-function potential. In the case of the repulsive two-component Bose gas we obtain a simple system of two NLIE allowing for an efficient numerical implementation in contrast with the infinite number of coupled equations obtained by employing the Thermodynamic Bethe Ansatz. Our technique makes use of the Quantum Transfer Matrix and the fact that in a certain continuum limit multi-component gases can be obtained from appropriate anisotropic spin chains.Comment: 4.3 pages, RevTeX 4.