4,767 research outputs found
On certain questions of the free group automorphisms theory
Certain subgroups of the groups of automorphisms of a free group
are considered. Comparing Alexander polynomials of two poly-free groups
and we prove that these groups are not isomorphic, despite the
fact that they have a lot of common properties. This answers the question of
Cohen-Pakianathan-Vershinin-Wu from \cite{CVW}. The questions of linearity of
subgroups of are considered. As an application of the properties of
poison groups in the sense of Formanek and Procesi, we show that the groups of
the type for certain groups and the subgroup of
-automorphisms are not linear for . This
generalizes the recent result of Pettet that are not linear for
.Comment: 11 page
Asymptotic behavior of photoionization cross section in a central field
We demonstrate that the high energy nonrelativistic asymptotic for the
photoionization cross section in a central field can be expressed in
terms of the asymptotic of the Fourier transform of the field. We show
that the cross sections drop in the same way for the fields with the Coulomb
short distance behavior. The character of the cross sections energy behavior is
related to the analytical properties of the function . The cross sections
exhibit power drop for the potentials which have singularities an the real
axis. They suffer the exponential drop if has singularities in the
complex plane.Comment: 11 page
Asymptotic behavior of photoionization cross section in a central field. Ionization of the states
We continue our studies of the high energy nonrelativistic asymptotics for
the photoionization cross section of the systems bound by a central field
. We consider the bound states with the orbital momentum . We
show, that as well as for the states the asymptotics can be obtained
without solving of the wave equations for the bound and outgoing electrons. The
asymptotics of the cross sections is expressed in terms of the asymptotics of
the Fourier transform of the field and its derivative by
employing the Lippmann--Schwinger equation. The shape of the energy dependence
of the cross sections is determined by the analytical properties of the
potential . The cross sections exhibit power drop with the increase of
the photon energy for the potentials which have singularities on the
real axis. They experience exponential drop if has poles in the complex
plane. We trace the energy dependence of the ratios of the photoionization
cross sections for and electrons from the states with the same
principle quantum number. We apply the results to the physics of fullerenes.Comment: 14 page
Nonlinear optical response in gapped graphene
We present a formulation for the nonlinear optical response in gapped
graphene, where the low-energy single-particle spectrum is modeled by massive
Dirac theory. As a representative example of the formulation presented here, we
obtain closed form formula for the third harmonic generation (THG) in gapped
graphene. It turns out that the covariant form of the low-energy theory gives
rise to a peculiar logarithmic singularities in the nonlinear optical spectra.
The universal functional dependence of the response function on dimension-less
quantities indicates that the optical nonlinearity can be largely enhanced by
tuning the gap to smaller values.Comment: http://iopscience.iop.org/0953-8984/labtalk-article/4938
Darboux transformation with dihedral reduction group
We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting BĂ€cklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix, we obtain local conservation laws of the system
Plane wave limit of local conserved charges
We study the plane wave limit of the Backlund transformations for the
classical string in AdS space times a sphere and obtain an explicit expression
for the local conserved charges. We show that the Pohlmeyer charges become in
the plane wave limit the local integrals of motion of the free massive field.
This fixes the coefficients in the expansion of the anomalous dimension as the
sum of the Pohlmeyer charges.Comment: v2: added explanation
Photoionization of helium-like ions in asymptotic nonrelativistic region
The cross section for single K-shell ionization by a high-energy photon is
evaluated in the next-to-leading order of the nonrelativistic perturbation
theory with respect to the electron-electron interaction. The screening
corrections are of particular importance for light helium-like ions. Even in
the case of neutral He atom, our analytical predictions turn out to be in good
agreement with the numerical calculations performed with the use of the
sophisticated wave functions. The universal high-energy behavior is studied for
the ratio of double-to-single photoionization cross sections. We also discuss
the fast convergence of the perturbation theory over the reversed nuclear
charge number 1/Z.Comment: 12 pages, 1 figure. to be published in Physics Letters
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