21,584 research outputs found
Skein theory for SU(n)-quantum invariants
For any n>1 we define an isotopy invariant, _n, for a certain set of
n-valent ribbon graphs Gamma in R^3, including all framed oriented links. We
show that our bracket coincides with the Kauffman bracket for n=2 and with the
Kuperberg's bracket for n=3. Furthermore, we prove that for any n, our bracket
of a link L is equal, up to normalization, to the SU_n-quantum invariant of L.
We show a number of properties of our bracket extending those of the Kauffman's
and Kuperberg's brackets, and we relate it to the bracket of
Murakami-Ohtsuki-Yamada. Finally, on the basis of the skein relations satisfied
by _n, we define the SU_n-skein module of any 3-manifold M and we prove that
it determines the SL_n-character variety of pi_1(M).Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-36.ab
Fractional Flux Periodicity in Doped Carbon Nanotubes
An anomalous magnetic flux periodicity of the ground state is predicted in
two-dimensional cylindrical surface composed of square and honeycomb lattice.
The ground state and persistent currents exhibit an approximate fractional
period of the flux quantum for a specific Fermi energy. The period depends on
the aspect ratio of the cylinder and on the lattice structure around the axis.
We discuss possibility of this nontrivial periodicity in a heavily doped
armchair carbon nanotube.Comment: 5 pages, 4 figure
Stabilization mechanism of edge states in graphene
It has been known that edge states of a graphite ribbon are zero-energy,
localized eigen-states. We show that next nearest-neighbor hopping process
decreases the energy of the edge states at zigzag edge with respect to the
Fermi energy. The energy reduction of the edge states is calculated
analytically by first-order perturbation theory and numerically. The resultant
model is consistent with the peak of recent scanning tunneling spectroscopy
measurements.Comment: 4 pages, 2 figures, final version to appear in Applied Physics
Letter
Electron impact on K+: mechanisms for extreme ultraviolet submission
A series of R-matrix calculations on K+ is used to derive electron excitation and ionization cross sections. The excitation cross section to the 4s and 3d levels leading to the K+ 60.1, 60.8 and 61.3nm emission lines shows poor agreement with the cross beam experiment of Zapesochny et al (1986, Zh. Eksp. Teor. Fiz. 90 1972 [Sov. Phys. JETP 63 1155]). Cross sections are also presented for exciting the 4p, 5s and 4d levels, the autoionizing 3s open-shell levels, and for ionization. It is shown how pseudoresonances in the calculated cross section can be eliminated by increasing the target
basis.</p
Well-localized edge states in two-dimensional topological insulators: ultrathin Bi films
We theoretically study the generic behavior of the penetration depth of the
edge states in two-dimensional quantum spin Hall systems. We found that the
momentum-space width of the edge-state dispersion scales with the inverse of
the penetration depth. As an example of well-localized edge states, we take the
Bi(111) ultrathin film. Its edge states are found to extend almost over the
whole Brillouin zone. Correspondingly, the bismuth (111) 1-bilayer system is
proposed to have well-localized edge states in contrast to the HgTe quantum
well.Comment: 4 pages, 4 figure
Intrinsic Spin Hall Effect in the Two Dimensional Hole Gas
We show that two types of spin-orbit coupling in the 2 dimensional hole gas
(2DHG), with and without inversion symmetry breaking, contribute to the
intrinsic spin Hall effect\cite{murakami2003,sinova2003}. Furthermore, the
vertex correction due to impurity scattering vanishes in both cases, in sharp
contrast to the case of usual Rashba coupling in the electron band. Recently,
the spin Hall effect in a hole doped semiconductor has been observed
experimentally by Wunderlich \emph{et al}\cite{wunderlich2004}. From the fact
that the life time broadening is smaller than the spin splitting, and the fact
impurity vertex corrections vanish in this system, we argue that the observed
spin Hall effect should be in the intrinsic regime.Comment: Minor typos fixed, one reference adde
Theory of "Jitter" Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks
Abridged.-- We demonstrate that the radiation emitted by ultrarelativistic
electrons in highly nonuniform, small-scale magnetic fields is different from
synchrotron radiation if the electron's transverse deflections in these fields
are much smaller than the beaming angle. A quantitative analytical theory of
this radiation, which we refer to as jitter radiation, is developed. It is
shown that the emergent spectrum is determined by statistical properties of the
magnetic field. As an example,we then use the model of a magnetic field in
internal shocks of GRBs. The spectral power distribution of radiation produced
by the power-law electrons is well described by a sharply broken power-law with
indices 1 and -(p-1)/2 and the jitter break frequency is independent of the
field strength but depends on the electron density in the ejecta. Since
large-scale fields may also be present in the ejecta, we construct a
two-component, jitter+synchrotron spectral model of the prompt -ray
emission. Quite surprisingly, this model seems to be readily capable of
explaining several properties of time-resolved spectra of some GRBs, such as
(i) the violation of the constraint on the low-energy spectral index called the
synchrotron ``line of death'', (ii) the sharp spectral break at the peak
frequency, inconsistent with the broad synchrotron bump, (iii) the evidence for
two spectral sub-components, and (iv) possible existence of emission features
called ``GRB lines''. We believe these facts strongly support both the
existence of small-scale magnetic fields and the proposed radiation mechanism
from GRB shocks. As an example, we use the composite model to analyze GRB
910503 which has two spectral peaks.Comment: 12 pages (emulateapj), 11 figures (EPS), ApJ, accepted. For related
work, see http://cfa-www.harvard.edu/~mmedved
Existence of an upper limit on the density of excitons in carbon nanotubes by diffusion-limited exciton-exciton annihilation: Experiment and theory
Through an investigation of photoemission properties of highly-photoexcited
single-walled carbon nanotubes, we demonstrate that there is an upper limit on
the achievable excitonic density. As the intensity of optical excitation
increases, all photoluminescence emission peaks arising from different
chirality single-walled carbon nanotubes showed clear saturation in intensity.
Each peak exhibited a saturation value that was independent of the excitation
wavelength, indicating that there is an upper limit on the excitonic density
for each nanotube species. We propose that this saturation behavior is a result
of efficient exciton-exciton annihilation through which excitons decay
non-radiatively. In order to explain the experimental results and obtain
excitonic densities in the saturation regime, we have developed a model, taking
into account the generation, diffusion-limited exciton-exciton annihilation,
and spontaneous decays of one-dimensional excitons. Using the model, we were
able to reproduce the experimentally obtained saturation curves under certain
approximations, from which the excitonic densities were estimated. The validity
of the model was confirmed through comparison with Monte Carlo simulations.
Finally, we show that the conventional rate equation for exciton-exciton
annihilation without taking into account exciton diffusion fails to fit the
experimentally observed saturation behavior, especially at high excitonic
densities.Comment: 5 figures, 1 tabl
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