A higher order analogue of the Carathéodory-Julia theorem

A higher order analogue of the classical Carathéodory-Julia theorem on boundary derivatives is proved.     

Stable particles in anisotropic spin-1 chains

Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to the phase boundary where a stable breather exists besides the stable particles, that form the Haldane triplet at the Heisenberg isotropic point. The numerical data, obtained by means of the Density Matrix Renormalization Group, confirm this picture in the so-called large-D phase for which we give also a quantitative analysis of the bound states using standard perturbation theory. However, the situation turns out to be considerably more intricate in the Haldane phase where, to the best of our data, we do not observe stable breathers contrarily to what could be expected from the sine-Gordon model, but rather only the three modes predicted by a novel anisotropic extension of the Non-Linear Sigma Model studied here by means of a saddle-point approximation.     

Beams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector - a complex combination of the electric and magnetic field vectors - that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.     

Polarization qubit phase gate in a coupled quantum-well nanostructure

We show that a giant Kerr nonlinearity with a relatively large cross phase modulation (CPM) phase-shift can be used for realizing polarization quantum phase gate based on the nonlinear optical response in a coupled semiconductor double quantum well (SDQW) structure via intersubband transitions.     

Cutting of multi walled carbon nanotubes

Multi walled carbon nanotubes (MCNT) synthesized by CVD method have been successfully cut into different lengths by controlling H₂SO₄/HNO₃ (5:3) oxidation time. During the cutting process H₂SO₄ and HNO₃ were added independently and the oxidation processes were carried out at a lower temperature to void excess weight loss and damage to MCNT. The resulting shorted MCNT (s-MCNT) formed stable dispersion state in the polar solvents without the help of surfactants that provided possibility for further functionalization and application. Moreover, NaOH solution was used to determine the total percentage of acidic sites and the total percentage of acidic sites are about 0.2-1%.     

The CP^1 nonlinear sigma model with ChernSimons term in the Faddeev-Jachiw quantization formalism

Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.     

Matrix Models and Matrix Integrals

We discuss the relations between arbitrary solutions of the loop equations describing the Hermitean one-matrix model and particular (multicut) solutions corresponding to concrete matrix integrals. These latter have a series of specific properties and, in particular, are described in terms of the Seiberg-Witten-Whitham theory. We consider the simplest example of an ordinary integral in detail. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 77–89, January, 2006.     

On the robustness of chaos in dynamical systems: Theories and applications

This paper offers an overview of some important issues concerning the robustness of chaos in dynamical systems and their applications to the real world.      

Weighted power counting and Lorentz violating gauge theories. I: General properties

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges a particular spacetime breaking, the one into space and time. We then concentrate on the simplest class of models, study four dimensional examples and discuss a number of issues that arise in our approach, such as the low-energy recovery of Lorentz invariance.