Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.     

Multicolor luminescence patterning by photoactivation of semiconductor nanoparticle films

Indiscriminate adsorption of nanoparticles (NPs) significantly complicates the preparation of mesoscale NP patterns considered as enabling technology for many devices and processes. Instead of selected chemical functionalization of the substrate surface prior to the assembly of nanocolloids, the required optical properties - in our case, high quantum yield luminescence - are imparted to the layer-by-layer assembled films by spatially selected photoactivation. The films are made by sequential adsorption of a positively charged polyelectrolyte and a negatively charged CdSe/CdS aqueous dispersion with an initial quantum yield of 0.5-2%. The photoactivation process takes place in the presence of oxygen and may be accompanied by photoetching. A 50-500-fold increase in the luminescence intensity of CdSe/CdS citrate-stabilized particles (quantum yield 25-45%) after visible light illumination provides excellent pattern contrast. Micron scale luminescence patterns were produced from NPs of various CdSe core diameters with red, yellow, and green emission. It was also demonstrated that different emission colors such as orange and green can be combined in one image by taking advantage of spatially selective photoetching. The presented optical patterning technique significantly simplifies the preparation of luminescence patterns as compared to conventional methods. The high signal-to-noise ratio associated with it is essential for optical devices, information processing, and biophotonics. The most immediate use of this approach is expected in cryptography and cell monitoring.     

Interference method of measuring the extinction coefficient of birefringent optical fibers

The extinction coefficient of a birefringent optical fiber (the ratio between the radiation power output of the polarization mode and the radiation power transferred from this mode to another one) characterizes the capability of a birefringent fiber to retain the polarization state of the radiation. In relatively short birefringent fibers (1–100 m), the extinction coefficient may reach 10⁴–10⁶. Such high values of the extinction coefficient are difficult to measure by standard techniques (excitation of one polarization mode by an incoherent source with subsequent recording of the light intensity at the output of the analyzer). An interference method of measuring the extinction coefficient of birefringent fibers is suggested. It is based on using a coherent source and measuring interference oscillations caused by an additional phase modulation at the input of the fiber. This method does not require precise polarization matching between the laser source and fiber and considerably loosens requirements for the polarizer-analyzer extinction and resolution of the photodetector. As a result, using simple standard components (semiconductor laser, film polarizer, and photodetector), one can measure extinction coefficient as high as 10⁶. The suggested interference method of measuring the extinction coefficient of birefringent fibers receives a theoretical analysis, and experimental data obtained for 2- to 1000-m-long fibers are presented.     

Total cross sections for fission of heavy nuclei by intermediate-energy protons

The results of measuring total cross sections for proton-induced fission of ^natPb, ²⁰⁹Bi, ²³²Th, ²³³U, ²³⁵U, ²³⁸U, ²³⁷Np, and ²³⁹Pu nuclei at proton energies from 200 to 1000 MeV are reported. The measurements were carried out in steps of ≈100 MeV. Complementary fission fragments were detected in coincidence by two parallel-plate avalanche gas counters placed in the beam line on both sides of the thin target close to it. Energy and isotope dependences of the fission cross sections are analyzed.     

Transport of ions of pyrophosphoric acid through chemically different anion-exchange membranes

Characteristics of mass transport of the anions of pyrophosphoric acid are investigated during electrodialysis through MA-40 and MA-41 anion-exchange membranes. It is established that the rate of mass transport for counterions is greater through the MA-41 membrane than the MA-40 membrane, and thus the former can be used for demineralizing solutions with salts of pyrophosphoric acid. Higher selectivity to pyrophosphate ions is found for the MA-40 membrane compared to the MA-41 membrane in the electrodialysis of mixtures of pyrophosphate and hydropyrophosphate ions, and thus the MA-40 membrane can be regarded as promising for the separation of such mixtures.     

Lie algebroid morphisms, Poisson sigma models, and off-shell closed gauge symmetries

Chern–Simons (CS) gauge theories in three dimensions and the Poisson sigma model (PSM) in two dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of the PSM in the literature are not globally well defined for non-parallelizable Poisson manifolds and propose a covariant definition of the off-shell gauge symmetries as left action of some finite-dimensional Lie algebroid.

Our approach allows us to avoid complications arising in the infinite-dimensional super-geometry of the BV- and AKSZ-formalism. This preprint is a starting point in a series of papers meant to introduce Yang–Mills type gauge theories of Lie algebroids, which include the standard YM theory, gerbes, and the PSM.