A new potential energy surface is presented for the triplet state 3At of the chemical reaction S（3P）＋H2 from a set of accurate ab initio data. The single point energies are computed using highly correlated complete...A new potential energy surface is presented for the triplet state 3At of the chemical reaction S（3P）＋H2 from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference configuration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8-2.2 eV. Both the centrifugalsudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H2 initially in the vibrational states v=0-3 （j=0）. It is found that initial vibrational excitation enhances the title reaction.展开更多
Dynamics of the Au + H2 reaction are studied using time-dependent wave packet(TDWP) and quasi-classical trajectory(QCT) methods based on a new potential energy surface [Int. J. Quantum Chem. 118 e25493(2018)]. The dyn...Dynamics of the Au + H2 reaction are studied using time-dependent wave packet(TDWP) and quasi-classical trajectory(QCT) methods based on a new potential energy surface [Int. J. Quantum Chem. 118 e25493(2018)]. The dynamic properties such as reaction probability, integral cross section, differential cross section and the distribution of product are studied at state-to-state level of theory. Furthermore, the present results are compared with the theoretical studies available.The results indicate that the complex-forming reaction mechanism is dominated in the reaction in the low collision energy region and the abstract reaction mechanism plays a dominant role at high collision energies. Different from previous theoretical calculations, the side-ways scattering signals are found in the present work and become more and more apparent with increasing collision energy.展开更多
We present a fully time-dependent quantum wave packet evolution method for investigating molecular dynamics in intense laser fields.This approach enables the simultaneous treatment of interactions among multiple elect...We present a fully time-dependent quantum wave packet evolution method for investigating molecular dynamics in intense laser fields.This approach enables the simultaneous treatment of interactions among multiple electronic states while simultaneously tracking their time-dependent electronic,vibrational,and rotational dynamics.As an illustrative example,we consider neutral H_(2)molecules and simulate the laser-induced excitation dynamics of electronic and rotational states in strong laser fields,quantitatively distinguishing the respective contributions of electronic dipole transitions(within the classical-field approximation)and non-resonant Raman processes to the overall molecular dynamics.Furthermore,we precisely evaluate the relative contributions of direct tunneling ionization from the ground state and ionization following electronic excitation in the strong-field ionization of H_(2).The developed methodology shows strong potential for performing high-precision theoretical simulations of electronic-vibrational-rotational state excitations,ionization,and dissociation dynamics in molecules and their ions under intense laser fields.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S)based on the electronic ground state(^(2)A′)pot...The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S)based on the electronic ground state(^(2)A′)potential energy surface of the SH_(2)-ionic molecule.The collision energy dependent reaction probabilities and integral cross sections are obtained.The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies.The vibrational excitation and rotational excitation of the diatomic reagent H_(2) promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j=0,2,4,6,8,10,and the vibrational quantum number v=0,1,2,3,4.The numerical integral cross sections are quite consistent with the experimental data reported in previous work.展开更多
We investigate the diffractive paraxial wave equation with an external potential,utilizing self-similarity and variable separation methods.The exact solution to this evolution equation,expressed through Scorer functio...We investigate the diffractive paraxial wave equation with an external potential,utilizing self-similarity and variable separation methods.The exact solution to this evolution equation,expressed through Scorer functions,gives rise to the new Scorer beams.We explore the dynamics of counterpropagating Scorer beams,as promising optical wave packets,focusing on their compression behavior.The Scorer beams are characterized by two key parameters:the attenuation factor and the initial pulse width.By appropriately adjusting these parameters,significant beam compression can be achieved.Specifically,increasing the attenuation factor enhances compression and raises pulse amplitude,while reducing the initial pulse width further amplifies these effects.Along the way,we observe interesting interference patterns of the counterpropagating Scorer beams that have never been seen before.This study introduces a novel approach to beam compression and opens new possibilities for practical applications of Scorer beams.展开更多
The time-resolved photoelectron spectrum (TRPES) of Rbl molecule is simulatedusing the time-dependent wave-packet method. Both the normal three-photon ionization process andauto-ionization process are involved in the ...The time-resolved photoelectron spectrum (TRPES) of Rbl molecule is simulatedusing the time-dependent wave-packet method. Both the normal three-photon ionization process andauto-ionization process are involved in the simulation. The calculated results show that the changeof delay time will influence the shape of the photoelectron spectrum (PES), and the influence issubstantially due to the existence of the crossing between excited states and the strong laser fieldwhich will change the position of relevant curves.展开更多
Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.T...Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.The total and partial decay widths,lifetimes,rates and their dependence on initial vibrational states were obtained for HeI2 at low initial vibrational excited levels.Our calculations show that the calculated tota decay widths,lifetimes and rates agree well with those extrapolated from experimental data available The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior.The very short propagation time (less.than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state inter-action between the fragments on the vibrationally deexcited adiabatic potential surface.The final state interaction between the fragments is shown to play an important role in determining the final rotational distribution This interpreta tion clearly explains the dynamical effect that the final rotational distribution shifts to the lower rotational energy levels as the initial vibrational quantum number v increases.展开更多
A time dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H 2 and D 2 on a flat and static surface. The molecule surface interaction is described using a modified London ...A time dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H 2 and D 2 on a flat and static surface. The molecule surface interaction is described using a modified London Eyring Polanyi Sato (LEPS) type potential for the H 2/Ni(100) system. The three dimensional (3 D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfy j+m =odd is forbidden at low energies for the homonuclear H 2 and D 2 due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in plane rotation (m=j) is more favorable for dissociation than the out of plane rotation (m=0) . Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H 2 when compared to D 2 were explained reasonably in terms of quantum mechanical zero point energies, the tunneling effect and the reflection from an activation barrier.展开更多
Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function in...Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range,particularly involving ultra-low energy.In this work,a new transparent boundary condition(TBC)is proposed for the time-dependent wave packet method.It in principle is of spectral accuracy when typical discrete variable representations are applied.The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function,in contrast with the complex absorbing potential.Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well,which supports resonances states.展开更多
The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first tr...The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.展开更多
This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beam- wave interaction. The radio frequency electromagnetic fields are represented as the superposition of azim...This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beam- wave interaction. The radio frequency electromagnetic fields are represented as the superposition of azimuthally sym- metric waves in a vacuum sheath helix. Coupling impedance is introduced to the electromagnetic field equations＇ stimulating sources, which makes the theory easier and more flexible to realize. The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations. The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included. The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields, focusing fields and space-charge fields. The numerically simulated results of a tube are presented.展开更多
On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion tha...On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.展开更多
A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of...A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory.展开更多
Evolution of periodic waves and solitary waves in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method...Evolution of periodic waves and solitary waves in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions.The results in this paper include some in the literatures [Phys. Rev. Lett. 94 （2005） 050402 and Chin. Phys. Left. 22 （2005） 1855].展开更多
Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-...Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.展开更多
Employing the two-state model and the time-dependent wave packet method, we have investigated the influences of the parameters of the intense femtosecond laser field on the evolution of the wave packet, as well as the...Employing the two-state model and the time-dependent wave packet method, we have investigated the influences of the parameters of the intense femtosecond laser field on the evolution of the wave packet, as well as the population of ground and double-minimum electronic states of the NaRb molecule. For the different laser wavelengths, the evolution of the wave packet of 6{ }^1／Sigma ^ ＋ state with time and internuclear distance is different, and the different laser intensity brings different influences on the population of the electronic states of the NaRb molecule. One can control the evolutions of wave packet and the population in each state by varying the laser parameters appropriately, which will be a benefit for the light manipulation of atomic and molecular processes.展开更多
The time-dependent wave packet method is used to investigate the influence of laser-fields on the vibrational population of molecules. For a two-state system in laser fields, the populations on different vibrational l...The time-dependent wave packet method is used to investigate the influence of laser-fields on the vibrational population of molecules. For a two-state system in laser fields, the populations on different vibrational levels of the upper and lower electronic states are given by wavefunctions obtained by solving the Schrbdinger equation with the split- operator method. The calculation shows that the field parameters, such as intensity, wavelength, duration, and delay time etc. can have different influences on the vibrational population. By varying the laser parameters appropriately one can control the evolution of wave packet and so the vibrational population in each state, which will benefit the light manipulation of atomic and molecular processes.展开更多
The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength ...The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength and intensity of laser pulse, the population of each state changing with time is obtained. The photo-absorption spectra and kinetic- energy distribution of the dissociation fragments, which exhibit vibration-level structure and dispersion of the wave packet, respectively, are also obtained. The results show that by increasing the laser intensity, one can find not only the band center shift of the photo-absorption spectrum, but also the change of the fragment energy. The appearance of the diffusive band in the photo-absorption spectrum and the multiple peaks in the kinetic-energy spectrum can be attributed to the effects of the predissoeiation limit and the external field.展开更多
Wave packet dynamics of the Li2 molecule are investigated by using the time-dependent quantum wave packet method, and the time-resolved photoelectron spectra of the Li2 molecule are calculated. The time-resolved wave ...Wave packet dynamics of the Li2 molecule are investigated by using the time-dependent quantum wave packet method, and the time-resolved photoelectron spectra of the Li2 molecule are calculated. The time-resolved wave packet theory is used to reasonably interpret the phenomena of the photoelectron spectra for different parameters. Our calculation shows that the loss of the wave packets in the shelf state area of E1∑g＋ plays a prominent role in the process of photoionization with the increase of the delay time. Moreover, the oscillation of the wave packet on the E1∑g＋ curve symbolizes a decreasing process of energy.展开更多
文摘A new potential energy surface is presented for the triplet state 3At of the chemical reaction S（3P）＋H2 from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference configuration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8-2.2 eV. Both the centrifugalsudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H2 initially in the vibrational states v=0-3 （j=0）. It is found that initial vibrational excitation enhances the title reaction.
文摘Dynamics of the Au + H2 reaction are studied using time-dependent wave packet(TDWP) and quasi-classical trajectory(QCT) methods based on a new potential energy surface [Int. J. Quantum Chem. 118 e25493(2018)]. The dynamic properties such as reaction probability, integral cross section, differential cross section and the distribution of product are studied at state-to-state level of theory. Furthermore, the present results are compared with the theoretical studies available.The results indicate that the complex-forming reaction mechanism is dominated in the reaction in the low collision energy region and the abstract reaction mechanism plays a dominant role at high collision energies. Different from previous theoretical calculations, the side-ways scattering signals are found in the present work and become more and more apparent with increasing collision energy.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFA1602502)the National Natural Science Foundation of China(Grant No.12450404)。
文摘We present a fully time-dependent quantum wave packet evolution method for investigating molecular dynamics in intense laser fields.This approach enables the simultaneous treatment of interactions among multiple electronic states while simultaneously tracking their time-dependent electronic,vibrational,and rotational dynamics.As an illustrative example,we consider neutral H_(2)molecules and simulate the laser-induced excitation dynamics of electronic and rotational states in strong laser fields,quantitatively distinguishing the respective contributions of electronic dipole transitions(within the classical-field approximation)and non-resonant Raman processes to the overall molecular dynamics.Furthermore,we precisely evaluate the relative contributions of direct tunneling ionization from the ground state and ionization following electronic excitation in the strong-field ionization of H_(2).The developed methodology shows strong potential for performing high-precision theoretical simulations of electronic-vibrational-rotational state excitations,ionization,and dissociation dynamics in molecules and their ions under intense laser fields.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金supported by Liao Ning Revitalization Talents Program(No.XLYC2007094)the Liaoning Bai Qian Wan Talents Program,the Natural Science Foundation of Liaoning Province(No.2020-BS083)the National Natural Science Foundation of China(No.11874241)。
文摘The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S)based on the electronic ground state(^(2)A′)potential energy surface of the SH_(2)-ionic molecule.The collision energy dependent reaction probabilities and integral cross sections are obtained.The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies.The vibrational excitation and rotational excitation of the diatomic reagent H_(2) promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j=0,2,4,6,8,10,and the vibrational quantum number v=0,1,2,3,4.The numerical integral cross sections are quite consistent with the experimental data reported in previous work.
基金supported by the National Natural Science Foundation of China under Grant No.62275176the Natural Science Foundation of Guangdong Province,China,under Grant No.2022A1515010084+1 种基金by Key Projects of Basic Research and Applied Basic Research in Universities of Guangdong Province,China,under Grants Nos.2021ZDZX1118 and 2022ZDZX1079supported by the NPRP 13S-0121-200126 Project with the Qatar National Research Fund(a member of the Qatar Foundation).
文摘We investigate the diffractive paraxial wave equation with an external potential,utilizing self-similarity and variable separation methods.The exact solution to this evolution equation,expressed through Scorer functions,gives rise to the new Scorer beams.We explore the dynamics of counterpropagating Scorer beams,as promising optical wave packets,focusing on their compression behavior.The Scorer beams are characterized by two key parameters:the attenuation factor and the initial pulse width.By appropriately adjusting these parameters,significant beam compression can be achieved.Specifically,increasing the attenuation factor enhances compression and raises pulse amplitude,while reducing the initial pulse width further amplifies these effects.Along the way,we observe interesting interference patterns of the counterpropagating Scorer beams that have never been seen before.This study introduces a novel approach to beam compression and opens new possibilities for practical applications of Scorer beams.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.10474060 and 10574083) the Natural Science Foundation of Shandong Province of China (Grant No. Y2003A02).
文摘The time-resolved photoelectron spectrum (TRPES) of Rbl molecule is simulatedusing the time-dependent wave-packet method. Both the normal three-photon ionization process andauto-ionization process are involved in the simulation. The calculated results show that the changeof delay time will influence the shape of the photoelectron spectrum (PES), and the influence issubstantially due to the existence of the crossing between excited states and the strong laser fieldwhich will change the position of relevant curves.
文摘Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.The total and partial decay widths,lifetimes,rates and their dependence on initial vibrational states were obtained for HeI2 at low initial vibrational excited levels.Our calculations show that the calculated tota decay widths,lifetimes and rates agree well with those extrapolated from experimental data available The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior.The very short propagation time (less.than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state inter-action between the fragments on the vibrationally deexcited adiabatic potential surface.The final state interaction between the fragments is shown to play an important role in determining the final rotational distribution This interpreta tion clearly explains the dynamical effect that the final rotational distribution shifts to the lower rotational energy levels as the initial vibrational quantum number v increases.
文摘A time dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H 2 and D 2 on a flat and static surface. The molecule surface interaction is described using a modified London Eyring Polanyi Sato (LEPS) type potential for the H 2/Ni(100) system. The three dimensional (3 D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfy j+m =odd is forbidden at low energies for the homonuclear H 2 and D 2 due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in plane rotation (m=j) is more favorable for dissociation than the out of plane rotation (m=0) . Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H 2 when compared to D 2 were explained reasonably in terms of quantum mechanical zero point energies, the tunneling effect and the reflection from an activation barrier.
基金supported by the National Natural Science Foundation of China (No.21733006,No.21825303 and No.21688102)the Strategic Priority Research Program of Chinese Academy of Sciences (No.XDB17010200).
文摘Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range,particularly involving ultra-low energy.In this work,a new transparent boundary condition(TBC)is proposed for the time-dependent wave packet method.It in principle is of spectral accuracy when typical discrete variable representations are applied.The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function,in contrast with the complex absorbing potential.Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well,which supports resonances states.
基金National Natural Science Foundation (K19972 0 11)
文摘The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60601004,60801029,10876005,and60931001)
文摘This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beam- wave interaction. The radio frequency electromagnetic fields are represented as the superposition of azimuthally sym- metric waves in a vacuum sheath helix. Coupling impedance is introduced to the electromagnetic field equations＇ stimulating sources, which makes the theory easier and more flexible to realize. The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations. The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included. The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields, focusing fields and space-charge fields. The numerically simulated results of a tube are presented.
基金supported by the Meteorological Special Project of China(GYHY200806005)the National Natural Sciences Foundation of China(40805028,40675039,40575036)the Key Technologies R&D Program of China(2009BAC51B04)
文摘On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60601004, 60801029, 10876005, and 60931001)
文摘A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory.
基金The project supported by Natioual Natural Science Foundation of China under Grant Nos. 1057508 and 10302018 and the Natural Science Foundation of Zhejiang Province of China under Grant No. Y605056The authors would like to thank Prof. Sen-Yue Lou for helpful discussions.
文摘Evolution of periodic waves and solitary waves in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions.The results in this paper include some in the literatures [Phys. Rev. Lett. 94 （2005） 050402 and Chin. Phys. Left. 22 （2005） 1855].
基金Project supported by the BUPT Excellent Ph.D.Students Foundation(Grant No.CX2019201)the National Natural Science Foundation of China(Grant Nos.11772017 and 11805020)+1 种基金the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(Grant No.IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China(Grant No.2011BUPTYB02)。
文摘Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10674114 and 10604045)
文摘Employing the two-state model and the time-dependent wave packet method, we have investigated the influences of the parameters of the intense femtosecond laser field on the evolution of the wave packet, as well as the population of ground and double-minimum electronic states of the NaRb molecule. For the different laser wavelengths, the evolution of the wave packet of 6{ }^1／Sigma ^ ＋ state with time and internuclear distance is different, and the different laser intensity brings different influences on the population of the electronic states of the NaRb molecule. One can control the evolutions of wave packet and the population in each state by varying the laser parameters appropriately, which will be a benefit for the light manipulation of atomic and molecular processes.
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2006A23)the National Basic Research Program of China (Grant No. 2006CB806000)the Open Fund of the State Key Laboratory of High Field Laser Physics (Shanghai Institute of Optics and Fine Mechanics)
文摘The time-dependent wave packet method is used to investigate the influence of laser-fields on the vibrational population of molecules. For a two-state system in laser fields, the populations on different vibrational levels of the upper and lower electronic states are given by wavefunctions obtained by solving the Schrbdinger equation with the split- operator method. The calculation shows that the field parameters, such as intensity, wavelength, duration, and delay time etc. can have different influences on the vibrational population. By varying the laser parameters appropriately one can control the evolution of wave packet and so the vibrational population in each state, which will benefit the light manipulation of atomic and molecular processes.
基金Project supported by the National Natural Science Foundation of China(Grant No.11074151)the Doctoral Program Foundation of Institutions of Higher Education of China(Grant No.20123704110002)
文摘The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength and intensity of laser pulse, the population of each state changing with time is obtained. The photo-absorption spectra and kinetic- energy distribution of the dissociation fragments, which exhibit vibration-level structure and dispersion of the wave packet, respectively, are also obtained. The results show that by increasing the laser intensity, one can find not only the band center shift of the photo-absorption spectrum, but also the change of the fragment energy. The appearance of the diffusive band in the photo-absorption spectrum and the multiple peaks in the kinetic-energy spectrum can be attributed to the effects of the predissoeiation limit and the external field.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60977063 and 10574039)the Foundation for Key Program of Ministry of Education China (Grant No. 206084)+1 种基金the Innovation Scientists and Technicians Troop Construction Projects of Henan Province,China (Grant No. 084100510011)the Innovation Talents of Institution of Higher Education of Henan Province,China (Grant No. 2006KYCX002)
文摘Wave packet dynamics of the Li2 molecule are investigated by using the time-dependent quantum wave packet method, and the time-resolved photoelectron spectra of the Li2 molecule are calculated. The time-resolved wave packet theory is used to reasonably interpret the phenomena of the photoelectron spectra for different parameters. Our calculation shows that the loss of the wave packets in the shelf state area of E1∑g＋ plays a prominent role in the process of photoionization with the increase of the delay time. Moreover, the oscillation of the wave packet on the E1∑g＋ curve symbolizes a decreasing process of energy.
