Harmonic analysis and the Riemann-Roch theorem

This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional adelic theory we obtain the Riemann-Roch formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic

Highly polarized injection luminescence in forward-biased ferromagnetic-semiconductor junctions at low spin polarization of current

We consider electron tunneling from a nonmagnetic $n$-type semiconductor ($n$-S) into a ferromagnet (FM) through a very thin forward-biased Schottky barrier resulting in efficient extraction of electron spin from a thin $n$-S layer near FM-S interface at low spin polarization of the current. We show that this effect can be used for an efficient polarization radiation source in a heterostructure where the accumulated spin polarized electrons are injected from $n$-S and recombine with holes in a quantum well. The radiation polarization depends on a bias voltage applied to the FM-S junction.Comment: 4 pages, 2 figure

A class of spin injection-precession ultrafast nanodevices

Spin valve ultrafast spin injection devices are described: an amplifier, a frequency multiplier, and a square-law detector. Their operation is based on injection of spin polarized electrons from one ferromagnet to another through a semiconductor layer and spin precession of the electrons in the semiconductor layer in a magnetic field induced by a (base) current in an adjacent nanowire. The base current can control the emitter current between the magnetic layers with frequencies up to several 100 GHz.Comment: 4 pages, 2 figures; minor typos corrected; to appear in Appl. Phys. Letter

The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes

The low-energy electronic structure of icosahedral fullerenes is studied within the field-theory model. In the field model, the pentagonal rings in the fullerene are simulated by two kinds of gauge fields. The first one, non-abelian field, follows from so-called K spin rotation invariance for the spinor field while the second one describes the elastic flow due to pentagonal apical disclinations. For fullerene molecule, these fluxes are taken into account by introducing an effective field due to magnetic monopole placed at the center of a sphere. Additionally, the spherical geometry of the fullerene is incorporated via the spin connection term. The exact analytical solution of the problem (both for the eigenfunctions and the energy spectrum) is found.Comment: 9 pages, 2 figures, submitted to European Physical Journal

Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six and eight quark interactions is applied to study temperature effects (SU(3) flavor limit, massless case), and (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations. The mesonic spectra built on the spontaneously broken vacuum induced by the 't Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.Comment: 4 pages, 4 figures, prepared for the proceedings of Quark Matter 2008 - 20th International Conference on Ultra-Relativistic Nucleus Nucleus Collisions, February 4-10, Jaipur (India

On some questions related to the Krichever correspondence

We investigate various new properties and examples of one-dimensional and two-dimensional Krichever correspondence developed by Parshin. In particular, we give explicit examples of the Krichever-Parshin map for various plane curves, we introduce analogs of the Schur pairs in a two-dimensional local field and show that they are oft geometrical. At the end we investigate analogs of the KP hierarchy for two-dimensional local skew-fields with arbitrary commutation law instead of the usual law of Weyl algebra. We derive for these hierarchies new partial differential equations, which coincide with the usual KP equation for certain values of parameters.Comment: 13