Reduction Groups and Automorphic Lie Algebras

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates the name automorphic Lie algebras. For automorphic Lie algebras we present bases in which they are quasigraded and all structure constants can be written out explicitly. These algebras have a useful factorisations on two subalgebras similar to the factorisation of the current algebra on the positive and negative parts.Comment: 21 pages, standard LaTeX2e, corrected typos, accepted for publication in CMP - Communications in Mathematical Physic

Theory of the giant plasmon enhanced second harmonic generation in graphene and semiconductor two-dimensional electron systems

An analytical theory of the nonlinear electromagnetic response of a two-dimensional (2D) electron system in the second order in the electric field amplitude is developed. The second-order polarizability and the intensity of the second harmonic signal are calculated within the self-consistent-field approach both for semiconductor 2D electron systems and for graphene. The second harmonic generation in graphene is shown to be about two orders of magnitude stronger than in GaAs quantum wells at typical experimental parameters. Under the conditions of the 2D plasmon resonance the second harmonic radiation intensity is further increased by several orders of magnitude.Comment: 9 pages, 2 figure

Reductions of integrable equations on A.III-type symmetric spaces

We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic Lax operators to this symmetric space. The symmetries of the Lax operator are inherited by the fundamental analytic solutions and give a characterization of the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl

Propagation of edge magnetoplasmons in semiconductor quantum-well structures

The wavelength and the propagation length of the edge magnetoplasmons, running along the edge of a two-dimensional electron layer in a semiconductor quantum-well structure are theoretically studied as a function of frequency, magnetic field, electron density, mobility, and geometry of the structure. The results are intended to be used for analysis and optimization of operation of recently invented quantum-well microwave spectrometers operating at liquid-nitrogen temperatures (I. V. Kukushkin {\em et al}, Appl. Phys. Lett. {\bf 86}, 044101 (2005)).Comment: 4 pages, including 4 figures. Accepted for publication in Appl. Phys. Let

Quantum Theory of the Third-Harmonic Generation in Graphene

A quantum theory of the third-harmonic generation in graphene is presented. An analytical formula for the nonlinear conductivity tensor $\sigma^{(3)}_{\alpha\beta\gamma\delta}(\omega,\omega,\omega)$ is derived. Resonant maxima of the third harmonic are shown to exist at low frequencies $\omega\ll E_F/\hbar$, as well as around the frequency $\omega=2E_F/\hbar$, where $E_F$ is the Fermi energy in graphene. At the input power of a CO$_2$ laser ($\lambda\approx 10$ $\mu$m) of about 1 MW/cm$^2$ the output power of the third-harmonic ($\lambda\approx 3.3$ $\mu$m) is expected to be $\simeq 50$ W/cm$^2$.Comment: 5 pages, 3 figure

Graphene-based voltage-tunable coherent terahertz emitter

A portion of the electromagnetic wave spectrum between $\sim 0.1$ and $\sim 10$ terahertz (THz) suffers from the lack of powerful, effective, easy-to-use and inexpensive emitters, detectors and mixers. We propose a multilayer graphene -- boron-nitride heterostructure which is able to emit radiation in the frequency range $\sim 0.1-30$ THz with the power density up to $\sim 0.5$ W/cm$^2$ at room temperature. The proposed device is extremely thin, light, flexible, almost invisible and may completely cover the needs of science and technology in the sources of terahertz radiation.Comment: 4 pages, 4 figures, slightly modified version of the previous submissio

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

On a realization of {β}\{\beta\}-expansion in QCD

We suggest a simple algebraic approach to fix the elements of the $\{ \beta \}$-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N$^2$LO calculations in QCD with the MSSM gluino -- an additional degree of freedom. We derive the formulae of the $\{ \beta \}$-expansion for the nonsinglet Adler $D$-function and Bjorken polarized sum rules in the actual N$^3$LO within this quantum field theory scheme with the MSSM gluino and the scheme with the second additional degree of freedom. We discuss the properties of the $\{ \beta \}$-expansion for higher orders considering the N$^4$LO as an example.Comment: 14 pages, Introduction, Sec.2, Conclusion are significantly improve