Based on the algebraic dynamics solution of ordinary differential equations and integration of $\hat L$ , the symplectic algebraic dynamics algorithm s? n is designed, which preserves the local symplectic geometric structure of a Hamiltonian system and possesses the same precision of the na?ve algebraic dynamics algorithm ? n . Computer experiments for the 4th order algorithms are made for five test models and the numerical results are compared with the conventional symplectic geometric algorithm, indicating that s? n has higher precision, the algorithm-induced phase shift of the conventional symplectic geometric algorithm can be reduced, and the dynamical fidelity can be improved by one order of magnitude.
Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz = 0, n = 0, and m ≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.
In the five-level K-type atomic system, by using another control field to couple the excited level of the coupling transition to the sixth higher excited level, a six-level atomic system is constructed. In this system, the multiple electromagnetically induced two-photon transparency has been investigated. What is more, if choosing the parameters of the control fields properly the triple transparency window will reduce to a double one which means that the multiple electromagnetically induced two-photon transparency can be manipulated in this system. The physical interpretation of these phenomena is given in terms of the dressed states and the dark states.
This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the dispersion equations of the beam-wave interaction, it solves relativistic Lorentz equation and Maxwell＇s equations for appropriate boundary conditions. It has been found in this waveguide structure that the TM0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes. The interaction of the dispersion curves of the electromagnetic TM0m modes and the upper betatron modes is studied. The growth rates of the wave are obtained, and the effects of the beam radius, the beam energy, the plasma frequency, and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.
