1,119 research outputs found
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
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
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
Harmonic analysis on local fields and adelic spaces I
We develop a harmonic analysis on objects of some category of
infinite-dimensional filtered vector spaces over a finite field. It includes
two-dimensional local fields and adelic spaces of algebraic surfaces defined
over a finite field. The main result is the theory of the Fourier transform on
these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last
sectio
Gauge theory of disclinations on fluctuating elastic surfaces
A variant of a gauge theory is formulated to describe disclinations on
Riemannian surfaces that may change both the Gaussian (intrinsic) and mean
(extrinsic) curvatures, which implies that both internal strains and a location
of the surface in R^3 may vary. Besides, originally distributed disclinations
are taken into account. For the flat surface, an extended variant of the
Edelen-Kadic gauge theory is obtained. Within the linear scheme our model
recovers the von Karman equations for membranes, with a disclination-induced
source being generated by gauge fields. For a single disclination on an
arbitrary elastic surface a covariant generalization of the von Karman
equations is derived.Comment: 13 page
Low-temperature thermal conductivity in polycrystalline graphene
The low-temperature thermal conductivity in polycrystalline graphene is
theoretically studied. The contributions from three branches of acoustic
phonons are calculated by taking into account scattering on sample borders,
point defects and grain boundaries. Phonon scattering due to sample borders and
grain boundaries is shown to result in a -behaviour in the thermal
conductivity where varies between 1 and 2. This behaviour is found to
be more pronounced for nanosized grain boundaries.
PACS: 65.80.Ck, 81.05.ue, 73.43.C
Disclination vortices in elastic media
The vortex-like solutions are studied in the framework of the gauge model of
disclinations in elastic continuum. A complete set of model equations with
disclination driven dislocations taken into account is considered. Within the
linear approximation an exact solution for a low-angle wedge disclination is
found to be independent from the coupling constants of the theory. As a result,
no additional dimensional characteristics (like the core radius of the defect)
are involved. The situation changes drastically for 2\pi vortices where two
characteristic lengths, l_\phi and l_W, become of importance. The asymptotical
behaviour of the solutions for both singular and nonsingular 2\pi vortices is
studied. Forces between pairs of vortices are calculated.Comment: 13 pages, published versio
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