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 Bäcklund 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

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 $V(r)$ can be expressed in terms of the asymptotic of the Fourier transform $V(p)$ 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 $V(r)$. The cross sections exhibit power drop for the potentials which have singularities an the real axis. They suffer the exponential drop if $V(r)$ has singularities in the complex plane.Comment: 11 page

Asymptotic behavior of photoionization cross section in a central field. Ionization of the pp states

We continue our studies of the high energy nonrelativistic asymptotics for the photoionization cross section of the systems bound by a central field $V(r)$. We consider the bound states with the orbital momentum $\ell=1$. We show, that as well as for the $s$ 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 $V(p)$ of the field and its derivative $V'(p)$ 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 $V(r)$. The cross sections exhibit power drop with the increase of the photon energy for the potentials $V(r)$ which have singularities on the real axis. They experience exponential drop if $V(r)$ has poles in the complex plane. We trace the energy dependence of the ratios of the photoionization cross sections for $s$ and $p$ electrons from the states with the same principle quantum number. We apply the results to the physics of fullerenes.Comment: 14 page

Anomalous dimension and local charges

AdS space is the universal covering of a hyperboloid. We consider the action of the deck transformations on a classical string worldsheet in $AdS_5\times S^5$. We argue that these transformations are generated by an infinite linear combination of the local conserved charges. We conjecture that a similar relation holds for the corresponding operators on the field theory side. This would be a generalization of the recent field theory results showing that the one loop anomalous dimension is proportional to the Casimir operator in the representation of the Yangian algebra.Comment: 10 pages, LaTeX; v2: added explanations, reference

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

About universal scalings in double K-shell photoionization

We discuss the problem of the universal scalings in the double ionization of atomic K-shell electrons caused by absorption of a single photon. In particular, we envisage the following questions: Under which conditions and up to which accuracy the universal scalings are realized? Does it make sense to talk about different physical mechanisms in the double-ionization process? Finally, we present also the theoretical analysis of recent experimental measurements performed on neutral atoms. As a testing ground, QED perturbation theory is employed.Comment: 5 pages, 4 figure

Endpoint behavior of the pion distribution amplitude in QCD sum rules with nonlocal condensates

Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its "integral" derivatives---defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region $x\sim 0$. The results for endpoint-suppressed and flat-top (or flat-like) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement---flat-type or CZ-like---yield values outside this range.Comment: 20 pages, 10 figures, 1 table, conclusions update