Transport in two dimensional electronic micro-emulsions

In two dimensional electron systems with Coulomb or dipolar interactions, a direct transition, whether first or second order, from a liquid to a crystalline state is forbidden. As a result, between these phases there must be other (micro-emulsion) phases which can be viewed as a meso-scale mixture of the liquid and crystalline phases. We investigate the transport properties of these new electronic phases and present arguments that they are responsible for the various transport anomalies that have been seen in experiments on the strongly correlated 2DEG in high mobility semiconductor devices with low electron densities.     

Quantum-algebras and elliptic algebras

We define a quantum-algebra associated to as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of , or theq-deformed classical-algebra algebra of . We construct free field realizations of the quantum-algebra and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in.The research of the second author was partially supported by NSF grant DMS-9501414.     

Modified construction of nuclear Fréchet spaces without basis

Recently, B. Mitiagin and N. Zobin constructed an example of nuclear Fréchet space without basis. The essential modification of their constructions gives the following results. There exists such a nuclear Fréchet space X that for any nuclear Fréchet space Y the space X × Y has no basis (Sections 1 and 2). This fact has a lot of corollaries (Sect. 3); e.g., the space X × C^∞(R¹) having the maximal diametral dimension among nuclear Fréchet spaces nevertheless has no basis. One can also construct (Sect. 4) a nuclear Fréchet space $\text{X}\text{?}$ without strongly finite-dimensional decomposition (see Definition 0.1). In Section 5 some comments and open questions are given.     

Optimization‐free superoscillatory lens using phase and amplitude masks

A superoscillatory focusing lens has been experimentally demonstrated by optimizing Fresnel zone plates (FZP), with limited physical insight as to how the lens feature contributes to the focal formation. It is therefore imperative to establish a generalized viable account for both FZP (amplitude mask) and binary optics (phase mask). Arbitrary superoscillatory spots can now be customized and realized by a realistic optical device, without using optimization. It is counterintuitively found that high spatial frequency with small amplitude and destructive interference are favorable in superfocusing of a superoscillation pattern. The inevitably high sidelobe is pushed 15λ away from the central subwavelength spot, resulting in significantly enlarged field of view for viable imaging applications. This work therefore not only reveals the explicit physical role of any given metallic/dielectric rings but also provides an alternative design roadmap of superresolution imaging. The robust method is readily applicable in superthin longitudinally polarized needle light, quantum physics and information theory.     

Three‐dimensional visible‐light capsule enclosing perfect supersized darkness via antiresolution

Supersized darkness in three dimensions surrounded by all light in free space is demonstrated theoretically and experimentally in the visible regime. The object staying in the darkness is similar to staying in an empty light capsule because light just bypasses it by resorting to destructive interference. A binary‐optical system is designed and fabricated based on achieving antiresolution (AR), by which electromagnetic energy flux avoids and bends smoothly around a nearly perfect darkness region. AR remains an unexplored topic hitherto, in contrast to the super‐resolution for realizing high spatial resolution. This novel scheme replies on smearing out the point spread function and thus poses less stringent limitations upon the object's size and position since the created dark (zero‐field) area reach 8 orders of magnitude larger than λ² in cross‐sectional size. It functions very well with arbitrarily polarized beams in three dimensions, which is also frequency scalable in the whole electromagnetic spectrum.     

Characterization of Al(III) complexes with hematein in artistic alum logwood inks

The complexes between Al(III) and hematein, the main coloring matter in alum logwood inks, were characterized by Raman and ²⁷Al NMR (nuclear magnetic resonance) spectroscopies. Raman spectra of the crystallized complexes and of the compounds applied on a paper substrate are presented and assigned based on published data for the parent compounds. These Raman spectra show that the coordination of the hematein to the Al(III) ions takes place in both cases through the carbonyl and hydroxyl groups in the molecule, and that the aromatic rings are also involved in the interaction. The Raman spectra of the pure hematein–Al(III) complexes were found to be consistent with those recorded for a logwood ink prepared following a late 19th century recipe, using logwood chips instead of pure hematein, and applied on a paper substrate. These spectra can be used as references for the noninvasive identification of the compounds in works of art. ²⁷Al solid‐state NMR showed that the coordination of the Al(III) atoms in the crystallized powder is predominantly octahedral, while when applied on a paper substrate the colorant is present mainly as a tetrahedral complex, with an octahedral coordination also present in a smaller proportion. The fact that the predominant coordinations for the complexes in the crystallized material and for the ones present on the paper substrate are different is relevant for the study of the lightfastness and thermal stability of works of art bearing these media. Copyright © 2009 John Wiley & Sons, Ltd.     

Highly resolved fluid flows: "liquid plasmas" at the kinetic level

Fluid flow around an obstacle was observed at the kinetic (individual particle) level using "complex (dusty) plasmas" in their liquid state. These "liquid plasmas" have bulk properties similar to water (e.g., viscosity), and a comparison in terms of similarity parameters suggests that they can provide a unique tool to model classical fluids. This allows us to study "nanofluidics" at the most elementary-the particle-level, including the transition from fluid behavior to purely kinetic transport. In this (first) experimental investigation we describe the kinetic flow topology, discuss our observations in terms of fluid theories, and follow this up with numerical simulations.     

Superfluid-superfluid phase transitions in a two-component Bose-Einstein condensate

Depending on the Hamiltonian parameters, two-component bosons in an optical lattice can form at least three different superfluid phases in which both components participate in the superflow: a (strongly interacting) mixture of two miscible superfluids (2SF), a paired superfluid (PSF) vacuum, and (at a commensurate total filling factor) the super-counter-fluid (SCF) state. We study the universal properties of the 2SF-PSF and 2SF-SCF quantum phase transitions and show that (i) they can be mapped onto each other and (ii) their universality class is identical to the (d+1)-dimensional normal-superfluid transition in a single-component liquid. The finite-temperature 2SF-PSF(SCF) transitions and the topological properties of 2SF-PSF(SCF) interfaces are also discussed.     

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.