Cyclic Statistics In Three Dimensions

While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of ref. [1,2,3]. In this work we demonstrate the existence of ``cyclic'', or $Z_n$, {\it non-permutation group} statistics for a system of n > 2 identical, unknotted rings embedded in $R^3$. We make crucial use of a theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin

Non-linear phenomena in time-dependent density-functional theory: What Rabi physics can teach us

Through the exact solution of a two-electron system interacting with a monochromatic laser we prove that all adiabatic density functionals within time-dependent density-functional theory are not able to discern between resonant and non-resonant (detuned) Rabi oscillations. This is rationalized in terms of a fictitious dynamical exchange-correlation (xc) detuning of the resonance while the laser is acting. The non-linear dynamics of the Kohn-Sham system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We identify the source of this error in a contribution from the xc-functional to the non-linear equations describing the electron dynamics in an effective two-level system. The constraint of preventing the detuning introduces a new strong condition to be satisfied by approximate xc-functionals

An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold

It is well known that the inequivalent unitary irreducible representations (UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta sectors'' in theories of quantum gravity with fixed spatial topology. In this paper, we study several families of UIR's of $G$ and attempt to understand the physical implications of the resulting quantum sectors. The mapping class group of a three-manifold which is the connected sum of $\R^3$ with a finite number of identical irreducible primes is a semi-direct product group. Following Mackey's theory of induced representations, we provide an analysis of the structure of the general finite dimensional UIR of such a group. In the picture of quantized primes as particles (topological geons), this general group-theoretic analysis enables one to draw several interesting qualitative conclusions about the geons' behavior in different quantum sectors, without requiring an explicit knowledge of the UIR's corresponding to the individual primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an appendix proving the semi-direct product structure of the MCG, corrected an error in the characterization of the slide subgroup, reworded extensively. All our analysis and conclusions remain as befor

Nonlinear optical materials formed by push-pull (bi)thiophene derivatives functionalized with di(tri)cyanovinyl acceptor groups

Studies of the second-order nonlinear optical susceptibilities of six NLOphores bearing di(tri)cyanovinyl acceptor groups linked to (bi)thiophene heterocyclic donor systems were performed for the first time in polymethyl methacrylate (PMMA) matrices with a 1064 nm laser working in the 20 ns time pulse regime. Absorption spectra and DFT calculations were also performed. This multidisciplinary study showed that modulation of the optical (linear and nonlinear) properties can be achieved by increasing the length of the -conjugated heterocyclic system (thiophene vs. bithiophene), the strength of the electron donor groups (HMeO/EtOEt2N) as well as the strength of the electron acceptor moieties (DCV vs. TCV, two vs. three electron withdrawing cyano groups). Due to the relatively high second-order susceptibilities (0.08 to 6.45 pm/V), the studied push-pull chromophores can be denote as very potent NLOphores.Fundação para a Ciência e a Tecnologia (FCT

Magnetic hydrodynamics with asymmetric stress tensor

In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde

Two-Scale Kirchhoff Theory: Comparison of Experimental Observations With Theoretical Prediction

We introduce a non-perturbative two scale Kirchhoff theory, in the context of light scattering by a rough surface. This is a two scale theory which considers the roughness both in the wavelength scale (small scale) and in the scales much larger than the wavelength of the incident light (large scale). The theory can precisely explain the small peaks which appear at certain scattering angles. These peaks can not be explained by one scale theories. The theory was assessed by calculating the light scattering profiles using the Atomic Force Microscope (AFM) images, as well as surface profilometer scans of a rough surface, and comparing the results with experiments. The theory is in good agreement with the experimental results.Comment: 6 pages, 8 figure

A new application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces

The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the surface height. Calculations can be greatly simplified with the use of reduced Rayleigh equations, because one of the unknown fields can be eliminated. We derive a new set of four reduced equations for the scattering amplitudes, which are applied to the cases of a rough conducting surface, and to a slab where one of the boundary is a rough surface. As in the one-dimensional case, numerical simulations show the appearance of enhanced backscattering for these structures.Comment: RevTeX 4 style, 38 pages, 16 figures, added references and comments on the satellites peak

Orphan crops of archaeology-based crop history research

So-called ‘forgotten’ or ‘orphan’ crops are an important component of strategies aimed at preserving and promoting biodiversity. Knowledge of historical cultivation, usage, and geographic and evolutionary trajectories of plants, that is, crop history research, is important for the long-term success of such efforts. However, research biases in the crops chosen for study may present hurdles. This review attempts to systematically identify patterns in crop species representativeness within archaeology-based crop history research. A meta-analysis and synthesis of archaeo- botanical evidence (and lack thereof) is presented for 268 species known to have been cultivated for food prior to 1492 CE from the Mediterranean region to South Asia. We identified 39 genera with known crop plants in this geographical and histor- ical context that are currently absent from its archaeobotanical record, constituting ‘orphan’ crops of archaeobotany. In addition, a worldwide synthesis of crop species studied using geometric morphometric, archaeogenetic and stable isotope analyses of archaeological plant remains is presented, and biases in the species represented in these disciplines are discussed. Both disciplinary methodological biases and economic agenda-based biases affecting species representativeness in crop history research are apparent. This study also highlights the limited geographic diffusion of most crops and the potential for deeper historical perspectives on how crops become marginal- ized and ‘forgotten’