10,540 research outputs found
Next-nearest-neighbor Tight-binding Model of Plasmons in Graphene
In this paper we investigate the influence of the next-nearest-neighbor
coupling of tight-binding model of graphene on the spectrum of plasmon
excitations. The nearest-neighbor tight-binding model was previously used to
calculate plasmon spectrum in the next paper [1]. We expand the previous
results of the paper by the next-nearest-neighbor tight-binding model. Both
methods are based on the numerical calculation of the dielectric function of
graphene and loss function. Here we compare plasmon spectrum of the
next-nearest and nearest-neighbor tight-binding models and find differences
between plasmon dispersion of two models.Comment: LaTeX, 4 pages, 4 Fig
A renormalized Gross-Pitaevskii Theory and vortices in a strongly interacting Bose gas
We consider a strongly interacting Bose-Einstein condensate in a spherical
harmonic trap. The system is treated by applying a slave-boson representation
for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the
condensate wave function that describes the dilute regime (like the
conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate
the condensate density of a rotating condensate for both the vortex-free
condensate and the condensate with a single vortex and determine the critical
angular velocity for the formation of a stable vortex in a rotating trap.Comment: 13 pages, 5 figures; revision and extension, figure 2 adde
Convex Equipartitions via Equivariant Obstruction Theory
We describe a regular cell complex model for the configuration space
F(\R^d,n). Based on this, we use Equivariant Obstruction Theory to prove the
prime power case of the conjecture by Nandakumar and Ramana Rao that every
polygon can be partitioned into n convex parts of equal area and perimeter.Comment: Revised and improved version with extra explanations, 20 pages, 7
figures, to appear in Israel J. Mat
A Simple Explanation for the X(3872) Mass Shift Observed for Decay to D^{*0} {D^0}bar
We propose a simple explanation for the increase of approximately
3 MeV/c^2 in the mass value of the X(3872) obtained from
D^{*0} {D^0}bar decay relative to that obtained from decay to J/psi pi+ pi-.
If the total width of the X(3872) is 2-3 MeV, the peak position in the
D^{*0} {D^0}bar invariant mass distribution is sensitive to the final state
orbital angular momentum because of the proximity of the X(3872) to D^{*0}
{D^0}bar threshold. We show that for total width 3 MeV and one unit of orbital
angular momentum, a mass shift ~3 MeV/c^2 is obtained; experimental mass
resolution should slightly increase this value. A consequence is that
spin-parity 2^- is favored for the X(3872).Comment: 3.5 pages, 4 eps figure
The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes
We compute the complete Fadell-Husseini index of the 8 element dihedral group
D_8 acting on S^d \times S^d, both for F_2 and for integer coefficients. This
establishes the complete goup cohomology lower bounds for the two hyperplane
case of Gr"unbaum's 1960 mass partition problem: For which d and j can any j
arbitrary measures be cut into four equal parts each by two suitably-chosen
hyperplanes in R^d? In both cases, we find that the ideal bounds are not
stronger than previously established bounds based on one of the maximal abelian
subgroups of D_8.Comment: new version revised according to referee's comments, 44 pages, many
diagrams; a shorter version of this will appear in Topology and its
Applications (ATA 2010 proceedings
Tverberg plus constraints
Many of the strengthenings and extensions of the topological Tverberg theorem
can be derived with surprising ease directly from the original theorem: For
this we introduce a proof technique that combines a concept of "Tverberg
unavoidable subcomplexes" with the observation that Tverberg points that
equalize the distance from such a subcomplex can be obtained from maps to an
extended target space.
Thus we obtain simple proofs for many variants of the topological Tverberg
theorem, such as the colored Tverberg theorem of Zivaljevic and Vrecica (1992).
We also get a new strengthened version of the generalized van Kampen-Flores
theorem by Sarkaria (1991) and Volovikov (1996), an affine version of their
"j-wise disjoint" Tverberg theorem, and a topological version of Soberon's
(2013) result on Tverberg points with equal barycentric coordinates.Comment: 15 pages; revised version, accepted for publication in Bulletin
London Math. Societ
Optimal bounds for the colored Tverberg problem
We prove a "Tverberg type" multiple intersection theorem. It strengthens the
prime case of the original Tverberg theorem from 1966, as well as the
topological Tverberg theorem of Barany et al. (1980), by adding color
constraints. It also provides an improved bound for the (topological) colored
Tverberg problem of Barany & Larman (1992) that is tight in the prime case and
asymptotically optimal in the general case. The proof is based on relative
equivariant obstruction theory.Comment: 17 pages, 3 figures; revised version (February 2013), to appear in J.
European Math. Soc. (JEMS
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