On the Solution of Topological Landau-Ginzburg Models with c=3c=3

The solution is given for the $c=3$ topological matter model whose underlying conformal theory has Landau-Ginzburg model W=-\qa (x^4 +y^4)+\af x^2y^2. While consistency conditions are used to solve it, this model is probably at the limit of such techniques. By using the flatness of the metric of the space of coupling constants I rederive the differential equation that relates the parameter \af\ to the flat coordinate $t$. This simpler method is also applied to the $x^3+y^6$-model.Comment: 7p

Energy gap tuning in graphene on hexagonal boron nitride bilayer system

We use a tight binding approach and density functional theory calculations to study the band structure of graphene/hexagonal boron nitride bilayer system in the most stable configuration. We show that an electric field applied in the direction perpendicular to the layers significantly modifies the electronic structure of the whole system, including shifts, anticrossing and other deformations of bands, which can allow to control the value of the energy gap. It is shown that band structure of biased system may be tailored for specific requirements of nanoelectronics applications. The carriers' mobilities are expected to be higher than in the bilayer graphene devices.Comment: 10 pages, 7 figures, submitted to Physical Review

Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization, m(x,t), is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m_0 for x0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=P(x/t) and the profile develops a flat part (m=P=0) in the |x/t|1/2 while it expands with the maximum velocity, c_0=1, for m_0->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.Comment: RevTex, 8 pages, 3 ps figure

Finite-dimensional analogs of string s <-> t duality and pentagon equation

We put forward one of the forms of functional pentagon equation (FPE), known from the theory of integrable models, as an algebraic explanation to the phenomenon known in physics as st duality. We present two simple geometrical examples of FPE solutions, one of them yielding in a particular case the well-known Veneziano expression for 4-particle amplitude. Finally, we interpret our solutions of FPE in terms of relations in Lie groups.Comment: LaTeX, 12 pages, 6 eps figure

Donut and dynamic polarization effects in proton channeling through carbon nanotubes

We investigate the angular and spatial distributions of protons of the energy of 0.223 MeV after channeling through an (11,~9) single-wall carbon nanotube of the length of 0.2 $\mu$m. The proton incident angle is varied between 0 and 10 mrad, being close to the critical angle for channeling. We show that, as the proton incident angle increases and approaches the critical angle for channeling, a ring-like structure is developed in the angular distribution - donut effect. We demonstrate that it is the rainbow effect. When the proton incident angle is between zero and a half of the critical angle for channeling, the image force affects considerably the number and positions of the maxima of the angular and spatial distributions. However, when the proton incident angle is close to the critical angle for channeling, its influence on the angular and spatial distributions is reduced strongly. We demonstrate that the increase of the proton incident angle can lead to a significant rearrangement of the propagating protons within the nanotube. This effect may be used to locate atomic impurities in nanotubes as well as for creating nanosized proton beams to be used in materials science, biology and medicine.Comment: 17 pages, 14 figure

One-dimensional semirelativity for electrons in carbon nanotubes

It is shown that the band structure of single-wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity $u$= $10^8$cm/s replacing the light velocity. One-dimensional semirelativistic kinematics and dynamics of electrons in CNT is formulated. Two-band k.p Hamiltonian is employed to demonstrate that electrons in CNT experience a Zitterbewegung (trembling motion) in absence of external fields. This Zitterbewegung should be observable much more easily in CNT than its analogue for free relativistic electrons in vacuum.Comment: 4 pages no figure

Collective Modes of Massive Dirac Fermions in Armchair Graphene Nanoribbons

We report the plasmon dispersion characteristics of intrinsic and extrinsic armchair graphene nanoribbons of atomic width N = 5 using a p_z-orbital tight binding model with third-nearest-neighbor (3nn) coupling. The coupling parameters are obtained by fitting the 3nn dispersions to that of an extended Huckel theory. The resultant massive Dirac Fermion system has a band gap E_g \approx 64 meV. The extrinsic plasmon dispersion relation is found to approach a common dispersion curve as the chemical potential $\mu$ increases, whereas the intrinsic plasmon dispersion relation is found to have both energy and momentum thresholds. We also report an analytical model for the extrinsic plasmon group velocity in the q \rightarrow 0 limit