We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable ...We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable Novikov equation.We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures.Moreover,we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.展开更多
In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter canno...In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.展开更多
Many papers have been published on the study of orbital angular momentum(OAM)of the laser modes based on the Laguerre-Gaussian(LG)beam and helical phase plate or rotating cylindrical lens,and the principal ray of the ...Many papers have been published on the study of orbital angular momentum(OAM)of the laser modes based on the Laguerre-Gaussian(LG)beam and helical phase plate or rotating cylindrical lens,and the principal ray of the LG beam remains straight line.These ways are difficult to get a large OAM modes.In this paper,we propose a novel method to prepare a large OAM modes when the light propagates through a optical fiber winding around a curved path,and establish a theoretical framework based on the principal ray path changing.Firstly,we investigate three kinds of winding structure.Secondly,based on the analytical solutions and numerical calculations,we can find that the spiral body can achieve a large OAM temporal pulse.At the same time,based on the zero OAM diffraction diagram,we can obtain an improvement of resolving power beyond Rayleigh’s criterion.Finally,applying a large OAM diffraction pattern to realize 12-bitencodes,we can obtain a high-security optical information transfer system.展开更多
基金National Natural Science Foundation of China(Grants Nos.12271424 and 11871395)National Natural Science Foundation of China(Grants Nos.11971251,11631007 and 12111530003)。
文摘We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable Novikov equation.We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures.Moreover,we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.
文摘In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.
基金supported by the National Natural Science Foundation of China(Grant No.11504074)the State Key Laboratory of Quantum Optics and Quantum Optics Devices,Shanxi University(Grant No.KF202004).
文摘Many papers have been published on the study of orbital angular momentum(OAM)of the laser modes based on the Laguerre-Gaussian(LG)beam and helical phase plate or rotating cylindrical lens,and the principal ray of the LG beam remains straight line.These ways are difficult to get a large OAM modes.In this paper,we propose a novel method to prepare a large OAM modes when the light propagates through a optical fiber winding around a curved path,and establish a theoretical framework based on the principal ray path changing.Firstly,we investigate three kinds of winding structure.Secondly,based on the analytical solutions and numerical calculations,we can find that the spiral body can achieve a large OAM temporal pulse.At the same time,based on the zero OAM diffraction diagram,we can obtain an improvement of resolving power beyond Rayleigh’s criterion.Finally,applying a large OAM diffraction pattern to realize 12-bitencodes,we can obtain a high-security optical information transfer system.
