Equi-intensity Distribution of Optical Reflectance in a Fibrous Turbid Medium

doi:10.1364/AO.49.000838Light propagation in a fibrous anisotropic scattering medium is quite different from that in an isotropic medium. Both the anisotropic diffuse equation (ADE) and the continuous time random walk (CTRW) theory predict that the equi-intensity profiles of the surface reflectance have an elliptical shape in a fibrous turbid medium. In this study, we simulated the spatially resolved surface reflectance in a fibrous sample using a Monte Carlo model. A parametric equation was used to quantitatively characterize the geometric profiles of the reflectance patterns. The results indicated that the equi-intensity profiles of surface reflectance had elliptical shapes only when evaluated at distances far away from the incident point. The length ratio of the two orthogonal axes of the ellipse was not affected by the sample optical properties when the ratio of reduced scattering coefficients along the two axes is the same. But the relationship between the aforementioned two ratios was different from the predication of ADE theory. Only for fibers of small sizes did the fitted axes ratios approach the values predicted from the ADE theory.This project was supported in part by National Science Foundation (NSF) grant CBET0643190

Resolution of simple singularities yielding particle symmetries in a space-time

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The homological intersection graph of this cycles is the Dynkin graph of an ADE Lie group. The deformation of the simple singularity corresponds to ADE symmetry breaking. A 3+1-dimensional topological model of observation is constructed, transforming consistently under SL(2,C), as an evolving 3-dimensional system of world tubes, which connect ``possible points of observation". The existence of an initial singularity for the 4-dimensional space-time is related to its global topological structure. Associating the geometry of ADE singularities to the vertex structure of the topological model puts forward the conjecture on a likewise relation of inner symmetries of elementary particles to local space-time structure.Comment: 16 pages, LaTe

Rectification by charging -- the physics of contact-induced current asymmetry in molecular conductors

We outline the qualitatively different physics behind charging-induced current asymmetries in molecular conductors operating in the weakly interacting self-consistent field (SCF) and the strongly interacting Coulomb Blockade (CB) regimes. A conductance asymmetry arises in SCF because of the unequal mean-field potentials that shift a closed-shell conducting level differently for positive and negative bias. A very different current asymmetry arises for CB due to the unequal number of open-shell excitation channels at opposite bias voltages. The CB regime, dominated by single charge effects, typically requires a computationally demanding many-electron or Fock space description. However, our analysis of molecular Coulomb Blockade measurements reveals that many novel signatures can be explained using a {{simpler}} orthodox model that involves an incoherent sum of Fock space excitations and {\it{hence treats the molecule as a metallic dot or an island}}. This also reduces the complexity of the Fock space description by just including various charge configurations only, thus partially underscoring the importance of electronic structure, while retaining the essence of the single charge nature of the transport process. We finally point out, however, that the inclusion of electronic structure and hence well-resolved Fock space excitations is crucial in some notable examples.Comment: 12 pages, 10 figure

The dubious success of export subsidies for wheat

Farm produce ; Exports ; Export controls

On Structure Constants of sl(2)sl(2) Theories

Structure constants of minimal conformal theories are reconsidered. It is shown that {\it ratios} of structure constants of spin zero fields of a non-diagonal theory over the same evaluated in the diagonal theory are given by a simple expression in terms of the components of the eigenvectors of the adjacency matrix of the corresponding Dynkin diagram. This is proved by inspection, which leads us to carefully determine the {\it signs} of the structure constants that had not all appeared in the former works on the subject. We also present a proof relying on the consideration of lattice correlation functions and speculate on the extension of these identities to more complicated theories.Comment: 32 page

Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems

Full counting statistics (FCS) of charge transfer in mesoscopic systems has recently become a subject of significant interest, since it proves to reveal an important information about the system which can be hardly assessed by other means. While the previous research mostly addressed the FCS of non- interacting systems, the present paper deals with the FCS in the limit of strong interaction. In this Coulomb blockade limit the electron dynamics is known to be governed by a master equation. We develop a general scheme to evaluate the FCS in such case, this being the main result of the work presented. We illustrate the scheme, by applying it to concrete systems. For generic case of a single resonant level we establish the equivalence of scattering and master equation approach to FCS. Further we study a single Coulomb blockade island with two and three leads attached and compare the FCS in this case with our recent results concerning an open dot either with two and three terminals. We demonstrate that Coulomb interaction suppresses the relative probabilities of large current fluctuations.Comment: 17 pages, 16 figure