The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric group U1(4) U2(4) U3(4), we construct the Hamiltonian that includes not o...The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric group U1(4) U2(4) U3(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M12,M13 and M23, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C2HF.展开更多
The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by s...The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by solving a set of coupled nonlinear differential equations. For considering the contribution of the high power of and , we use the Magnus formula. Thus, with the time-evolution operators we can get the statistical average values of the measurable quantities in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of (rigid rotor) by a flat, rigid surface to illustrate its general procedure. The results demonstrate that the method is useful for describing the statistical dynamics of gas-surface scattering.展开更多
This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in ...This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.展开更多
We extend the Poincaré group to the complex Minkowski space-time. Special attention is paid to the corresponding algebra that we achieve through matrices as well as differential operators. We also point out the g...We extend the Poincaré group to the complex Minkowski space-time. Special attention is paid to the corresponding algebra that we achieve through matrices as well as differential operators. We also point out the generalizations of the two Casimir operators.展开更多
We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obt...We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.展开更多
An analytical expression of the propagator is obtained by using Lie algebramethod.The fission rates at the saddle point in both constant and coordinate-dependentmass,friction and temperature cases are calculated based...An analytical expression of the propagator is obtained by using Lie algebramethod.The fission rates at the saddle point in both constant and coordinate-dependentmass,friction and temperature cases are calculated based on the expression of thepropagator and local approximation.The numerical calculation for <sup>240</sup>pu shows thatthe fission rates from our method are reasonable.展开更多
Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the ext...Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the external field, and then simulate the trajectories of particles in the total field; the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes. Two simulation codes based on the two methods are developed respectively, and the simulated results of transport in a set of electrostatic lenses are compared. It is found that the results from the two codes are in agreement with each other, and both approaches have their own merits.展开更多
A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H2 on a static flat metal surface. An LEPS potential energy surface has been used to describe the intera...A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H2 on a static flat metal surface. An LEPS potential energy surface has been used to describe the interaction of H2 with Ni(100) surface. The dependence of the initial state-selected dissociation probability was obtained analytically on the initial kinetic energy and time. A comparison with other theoretical calculations and experiments is made. The results show that the method can be effectively used to describe the dynamics of reactive gas-surface scattering.展开更多
The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4)?U24. After rovibrational interactions being considered, the eigen...The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4)?U24. After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels ofv 2 band for transition (0200–0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm?1, respectively.展开更多
The highly excited vibrational states of quasi-linear tetraatomic molecule HCNO are studied in the framework of U(4) algebra. By using symmetric group with which the tetraatomic molecules satisfy, we construct the alg...The highly excited vibrational states of quasi-linear tetraatomic molecule HCNO are studied in the framework of U(4) algebra. By using symmetric group with which the tetraatomic molecules satisfy, we construct the algebraic Hamiltonian that not only includes Majorana operator M 12 but also M 13 and M 23 which are very useful for getting potential energy surface and force constants in Lie algebra method. And the eigenvalue of the Hamiltonian are obtained by Lie algebra treatment.展开更多
基金the National Natural Science Foundation of China (Grant No. 20173031)the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University at Changchun (Grant No. 9801)the Science Foundation of Shandong Province of China (Grant No.Y98B08027)
文摘The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric group U1(4) U2(4) U3(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M12,M13 and M23, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C2HF.
基金The project supported by Natural Science Foundation of Shandong Province of China+2 种基金National Natural Science Foundation of Chinathe Doctor Foundation of the Ministry of Education of China
文摘The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by solving a set of coupled nonlinear differential equations. For considering the contribution of the high power of and , we use the Magnus formula. Thus, with the time-evolution operators we can get the statistical average values of the measurable quantities in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of (rigid rotor) by a flat, rigid surface to illustrate its general procedure. The results demonstrate that the method is useful for describing the statistical dynamics of gas-surface scattering.
基金Project supported by the National Natural Science Foundation of China （Grant No 1057009）.
文摘This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.
文摘We extend the Poincaré group to the complex Minkowski space-time. Special attention is paid to the corresponding algebra that we achieve through matrices as well as differential operators. We also point out the generalizations of the two Casimir operators.
文摘We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.
文摘An analytical expression of the propagator is obtained by using Lie algebramethod.The fission rates at the saddle point in both constant and coordinate-dependentmass,friction and temperature cases are calculated based on the expression of thepropagator and local approximation.The numerical calculation for <sup>240</sup>pu shows thatthe fission rates from our method are reasonable.
基金Supported by National Natural Science Foundation of China (10075005)Specialized Research Fund for the Doctoral Program of Higher Education (20070001001)
文摘Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the external field, and then simulate the trajectories of particles in the total field; the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes. Two simulation codes based on the two methods are developed respectively, and the simulated results of transport in a set of electrostatic lenses are compared. It is found that the results from the two codes are in agreement with each other, and both approaches have their own merits.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19694033)partially by the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University (Grant No. 9801).
文摘A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H2 on a static flat metal surface. An LEPS potential energy surface has been used to describe the interaction of H2 with Ni(100) surface. The dependence of the initial state-selected dissociation probability was obtained analytically on the initial kinetic energy and time. A comparison with other theoretical calculations and experiments is made. The results show that the method can be effectively used to describe the dynamics of reactive gas-surface scattering.
基金the Natural Science Foundation of Shandong Province of China(Grant No.Y98B08027)the National Natural Science Foundation of China(Grant No.20173031).
文摘The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4)?U24. After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels ofv 2 band for transition (0200–0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm?1, respectively.
文摘The highly excited vibrational states of quasi-linear tetraatomic molecule HCNO are studied in the framework of U(4) algebra. By using symmetric group with which the tetraatomic molecules satisfy, we construct the algebraic Hamiltonian that not only includes Majorana operator M 12 but also M 13 and M 23 which are very useful for getting potential energy surface and force constants in Lie algebra method. And the eigenvalue of the Hamiltonian are obtained by Lie algebra treatment.
