We have studied structures of single walled carbon nanotubes and metal semiconductor transition for the symmetric breaking. It was found that band gap existed for metallic armchair single walled carbon nanotubes. Calculations were made to analyse the meta-stability of the corrugated structures of armchair single walled carbon nanotubes. The corrugated single walled carbon nanotube structures are always lower in energy than the non corrugated nanotubes. The curvature effect was that the corrugated structure breaks the local symmetry between different carbon atoms. A true gap is created which does not vanish even when an external magnetic field is swept. The corrugation length and band gap gaps are decaying functions of the nanotubes radius and approached zero for carbon nanotube such as graphene. This was also true for zigzag and chiral single wall carbon nanotubes. The obtained results were found in good agreement with previously obtained results.
Rabi waves for the excitation of quantum nanoantennas with electrically controlled radiation and frequency characteristics were studied. The operational frequency of the visible range was based on the high frequency component of the current. The low frequency component and its operational frequency was in the terahertz range. The feature of the Rabi wave antenna depends on the carrier frequency on the electromagnetic field intensity. The contribution of high order magnetic multipoles became essential. The radiation properties of an antenna were the same as the ideal magnetic dipole. The antenna frequency spectrum corresponded to the amplitude modulated Rabi oscillations. The high frequency current was in the optical range in the vicinity of the quantum transition frequency. The radiation field of the nano antenna was considered equivalent to the field of magnetic dipole placed in the centre of current ring and oriented orthogonal to the ring plane. The equivalence was consequence of the electrical smallness of the antenna over the working range of frequency. The results obtained were in good agreement with previous results.
We have studied the nonlinear interaction between two different eigen modes in suspended carbon nanotube resonators. It was found that the mode coupling in suspended carbon nanotubes was dominated by single electron-tunneling process. For suspended carbon nanotube resonator at low temperatures using quantum dot embedded in the nanotube as detector, the interaction was found between two different eigen modes. For nanotube resonators in the coulomb blockade regime the nonlinear modal interaction was dominated by single electron tunneling as opposed to displacement induced tension. A strongly enhanced mode coupling was observed in the coulomb blockade regime which was of the order of magnitude larger than in conventional micro resonators. The obtained results found in good agreement with previously obtained results.
We have studied the asymmetric transmission in diffractive chiral metasurfaces consisting of nanoantennas. The study was made of lattice plasmon modes on the phenomenon of asymmetric transmission in chiral two dimensional arrays of plasmonic nanoparticles. It was demonstrated that asymmetric transmission resulted from contribution of higher order diffracted waves. It was shown that the isolated nanostructures has a fourfold rotational symmetry, the diffractive metasurfaces exhibited asymmetric transmission for normal incidence light within spectral range for which lattice plasmon modes were supported. It was found that lattice plasmon modes played role in enabling symmetric transmission in diffractive chiral metasurfaces. The symmetric transmission mechanism is due to different lattice plasmon mode excitation efficiencies of left circularly polarized and right circularly polarized and right circularly polarized light. The excitation efficiencies are controlled by tailoring the nano particles in plan distribution of scattered light for circularly polarized excitation and its alignment with the inplane diffraction orders of the metasurfaces. The phenomenon for a metasurface composed of an array of a chiral nanoparticles consisting of four nanoantennas. It was shown that the Rayleigh anomaly condition where the asymmetric transmission effect was strongest and metasurfaces supported lattice plasmon modes. It was found that the difference in the inplane scattered intensity varied as a function of the inplane angle around the nanostructure, rotating the nanostructure in the plane of the metasurface. The obtained results found in good agreement with previously obtained results.
A detailed proof of the incorrectness of the classical wave equation is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: the classical wave equation and the derivation of the classical wave equation are a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable main results: (1) The first gross error is the following approximate relationship: “sine of angle is approximately equal to tangent of angle; cosine of angle is approximately equal to 1”. This relationship means (implies) that the quantity of the angle and the right-angled triangle do not exist. Consequently, the relationship between the tangent of the angle and the derivative of the displacement with respect to coordinate does not exist; (2) The second gross error is that the second-order derivative of the displacement with respect to coordinate does not exist, because the dimensions of displacement and coordinate are “meter”, the first-order derivative of the displacement with respect to coordinate is dimensionless quantity (i.e. the first-order derivative of the displacement respect to coordinate has no the dimension “meter”); (3) The third gross error is that the first-order derivative of the displacement with respect to coordinate cannot be expanded into the Taylor series, because the second-order derivative of the displacement with respect to coordinate does not exist; (4) The fourth gross error is as follows: (a) the left side of the wave equation contains the condition that time is a variable quantity, and the coordinate is a constant quantity; (b) the right side of the wave equation contains the condition that time is a constant, and the coordinate is a variable. This means (implies) that the equation contains contradictory conditions (propositions). Therefore, the equation represents a violation of the formal-logical law of the lack (absence) of contradiction; (5) The fifth gross error is that the standard derivation of the equation relies on the following false theories: negative number theory, complex numbers theory, trigonometry, vector calculus, differential calculus, and Newton's second law. Thus, the classical wave equation does not satisfy the criterion of truth and is not a scientific achievement.
