Kink solutions of two generalized fifth-order nonlinear evolution equations

In this paper, two generalized fifth-order nonlinear evolution equations are introduced and investigated: One is (1+1)-dimensional, the other is (2+1)-dimensional. The Hereman–Nuseir method is used to derive the multiple kink solutions and singular kink solutions, and the conditions for the cases of complete integrability of these two equations. Meanwhile, it is found that these equations have completely different dispersion relations and physical structures. The corresponding graphs with specific parameters are given to show the effectiveness and validness of the obtained results.

˄C˄C 4 He and ˄C˄C 4 H hypernuclei

In our article we consider charmed hypernuclei states having the number of baryons B = 4 and containing two Ae hyperons. To do this we use the technique of the dispersion relations. We obtain the relativistic equations which describe these states. The relativistic amplitudes for 12-quark states, including the constituent quarks of three flavors u, d, c are considered. We find the approximate solutions of these equations and take into account main singularities of the amplitudes. We calculate masses and binding energies of the hypernuclei states ˄C˄C 4 He, ˄C˄C 4 H.

The γπ → ππ anomaly from lattice QCD and dispersion relations

We propose a formalism to extract the γπ → ππ chiral anomaly F3π from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the γ(*)π → ππ amplitude, whose main quark-mass dependence arises from the ππ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the P-wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent γ(*)π → ππ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the ρ(770) meson and, for the first time, the chiral anomaly F3π = 38(16)(11) GeV−3. The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.

INFLUENCE OF THE THICKNESS OF THE n-Si SUBSTRATE AND ITS DOPING LEVEL ON THE ABSORBING PROPERTIES OF SILICON PLASMON STRUCTURES IN THE INFRARED RANGE

The absorption spectra of Si/SiO2/Si3N4/Si+ and Si/SiO2/Si+ structures with an island surface layer are calculated using the finite difference time domain method. The absorption spectra were modeled depending on the thickness of the substrate and its doping level. It was found that the thickness of the i-Si substrate does not affect the overall absorption of the structure. At the same time, an increase in the thickness of the n-Si substrate leads to an expansion of the absorption band with an intensity of more than 70%. It is established that the doping level of the substrate affects the absorption value of the structures and bandwidth with an absorption value above 80%. It is shown that a wide absorption band with intensity of more than 80% occurs at the doping level of the substrate in the range of 2 . 1019—5 . 1019 cm–3. Dispersion relations in the Si+/SiO2/Si+ structure with an unstructured surface layer are obtained. These dispersion relations may indicate the existence of plasmon oscillations in the system. It is established that a violation of the phase synchronization of the modes at both Si/dielectric interfaces at a significant difference between the doping levels of the substrate and the surface layer can lead to a decrease in the absorption.

Quantum Confinement of Chiral Charge Carriers in Ring Conductors

<p>We theoretically study the quantum confinement effects and transport prop- erties of quantum ring (QR) systems. In particular, we investigate QRs made out of the following materials: single-layer graphene (SLG), single- layer transition-metal dichalcogenides (TMDs) and narrow-gap semiconduc- tor quantum wells (SQWs). Via perturbation theory and assuming that the ring aspect ratio is small, the general subband dispersion relations of these hard-wall ring confined systems are determined. These dispersion results agree with and extend on previous works. We discover the necessity of including both a size-quantisation energy and an angular momentum dependent energy shift to the dispersion equation due to their sizeable impact on the conductance of the system. The topological properties of these QR systems is also investigated. We find that QR confinement of materials may destroy the topologically non-trivial properties of states. The topological phase can be recovered when the band structure is inverted and the confined material parameters satisfy certain critical widths and gap limits. An analytical expression of the conductance for QRs (with symmetrically- arranged leads), in the presence of the perpendicular magnetic field piercing the centre of the ring, is derived. We study the geometric (i.e. Berry) and dynamic phases of the system that arise from the interference of partial waves in the ring branches. We discover that the Berry phase is modified by a correction term that arises purely from the quantum confinement of the materials. This has generally not been taken into account by previous studies. The explicit analytical expressions of the phase correction term are derived and shown to be proportional to the angular momentum dependent energy shift, present in the dispersion relations, for lead injection energies close to the subband energy. Overall, this study finds that the material-dependent phase plays a significant role in both the dispersion relation and the conductance of QRs and thus provides a useful insight for future experimental efforts with regards to transport in QR systems.</p>

Quantum Confinement of Chiral Charge Carriers in Ring Conductors

<p>We theoretically study the quantum confinement effects and transport prop- erties of quantum ring (QR) systems. In particular, we investigate QRs made out of the following materials: single-layer graphene (SLG), single- layer transition-metal dichalcogenides (TMDs) and narrow-gap semiconduc- tor quantum wells (SQWs). Via perturbation theory and assuming that the ring aspect ratio is small, the general subband dispersion relations of these hard-wall ring confined systems are determined. These dispersion results agree with and extend on previous works. We discover the necessity of including both a size-quantisation energy and an angular momentum dependent energy shift to the dispersion equation due to their sizeable impact on the conductance of the system. The topological properties of these QR systems is also investigated. We find that QR confinement of materials may destroy the topologically non-trivial properties of states. The topological phase can be recovered when the band structure is inverted and the confined material parameters satisfy certain critical widths and gap limits. An analytical expression of the conductance for QRs (with symmetrically- arranged leads), in the presence of the perpendicular magnetic field piercing the centre of the ring, is derived. We study the geometric (i.e. Berry) and dynamic phases of the system that arise from the interference of partial waves in the ring branches. We discover that the Berry phase is modified by a correction term that arises purely from the quantum confinement of the materials. This has generally not been taken into account by previous studies. The explicit analytical expressions of the phase correction term are derived and shown to be proportional to the angular momentum dependent energy shift, present in the dispersion relations, for lead injection energies close to the subband energy. Overall, this study finds that the material-dependent phase plays a significant role in both the dispersion relation and the conductance of QRs and thus provides a useful insight for future experimental efforts with regards to transport in QR systems.</p>