1,090 research outputs found
Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
Spin Filtering via Resonant Reflection of Relativistic Surface States
A microscopic approach is developed to scattering of surface states from a
non-magnetic linear defect at a surface with strong spin-orbit interaction.
Spin-selective reflection resonances in scattering of Rashba-split surface
states by an atomic stripe are theoretically discovered in a proof-of-principle
calculation for a model crystal potential. Spin-filtering properties of such
linear defects are analyzed within an envelope-function formalism for a
perturbed surface based on the Rashba Hamiltonian. The continuous Rashba model
is found to be in full accord with the microscopic theory, which reveals the
essential physics behind the scattering resonance. The spin-dependent
reflection suggests a novel mechanism to manipulate spins on the nanoscale.Comment: 6 pages, 4 figures, 1 tabl
The quasiparticle band gap in the topological insulator Bi2Te3
We present a theoretical study of dispersion of states which form the bulk
band-gap edges in the three-dimensional topological insulator Bi2Te3. Within
density functional theory, we analyze the effect of atomic positions varying
within the error range of the available experimental data and approximation
chosen for the exchange-correlation functional on the bulk band gap and k-space
location of valence- and conduction-band extrema. For each set of the positions
with different exchange-correlation functionals, we show how many-body
corrections calculated within a one-shot GW approach affect the mentioned
characteristics of electronic structure of Bi2Te3. We thus also illustrate to
what degree the one-shot GW results are sensitive to the reference one-particle
band structure in the case of bismuth telluride. We found that for this
topological insulator the GW corrections enlarge the fundamental band gap and
for certain atomic positions and reference band structure bring its value in
close agreement with experiment.Comment: 12 pages, 6 figures, 5 table
On the limiting power of set of knots generated by 1+1- and 2+1- braids
We estimate from above the set of knots, , generated by
closure of n-string 1+1- and 2+1-dimensional braids of irreducible length
() in the limit n>>1.Comment: 14 LaTeX pages, 2 PostScript figure
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