Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equat...Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at down- stream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.展开更多
A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and ...A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The modes have high coherence of near-field pressure for both jets, while the coherence of modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.展开更多
In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudo...In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that applies only in the neighborhoods of the lowest two quantum resonances, the proposed theory is applicable in the neighborhoods of all quantum resonances in principle by considering the quantum effect of the free rotation at a quantum resonance. In particular, it is confirmed by simulations that the quantum wavepacket dynamics can be successfully forecasted based on the generalized pseudoclassical dynamics, offering an intriguing example where it is feasible to bridge the dynamics in the deep quantum regime to the classical dynamics. The application of the generalized pseudoclassical theory to the PT-symmetric kicked rotor is also discussed.展开更多
Non-spreading nature of Bessel spatiotemporal wavepackets is theoretically and experimentally investigated and orders of magnitude improvement in the spatiotemporal spreading has been demonstrated.The spatiotemporal c...Non-spreading nature of Bessel spatiotemporal wavepackets is theoretically and experimentally investigated and orders of magnitude improvement in the spatiotemporal spreading has been demonstrated.The spatiotemporal confinement provided by the Bessel spatiotemporal wavepacket is further exploited to transport transverse orbital angular momentum through embedding spatiotemporal optical vortex into the Bessel spatiotemporal wavepacket, constructing a new type of wavepacket: Bessel spatiotemporal optical vortex. Both numerical and experimental results demonstrate that spatiotemporal vortex structure can be well maintained and confined through much longer propagation. High order spatiotemporal optical vortices can also be better confined in the spatiotemporal domain and prevented from further breaking up, overcoming a potential major obstacle for future applications of spatiotemporal vortex.展开更多
This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite ...This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanica is shown explicitly in the system.展开更多
We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion...We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.展开更多
By means of WKB expansions, new fourth order evolution equations are derived for two-dimensional Stokes waves over the bottom with arbitrary depth. The effects of slowly varying depth h= h (ε~2 x) and current U=U(ε~...By means of WKB expansions, new fourth order evolution equations are derived for two-dimensional Stokes waves over the bottom with arbitrary depth. The effects of slowly varying depth h= h (ε~2 x) and current U=U(ε~2x, ε~2t, ε~4z) on the evolution of a packet of Stokes waves are considered as well. In addition, numerical simulation is performed for the evolution of single envelope by finite-difference method.展开更多
The forms of minimum wavepackets (MWPs) corresponding to the geueralized momentum space and coordinates spaca are derived by using the generalized Hermitian expression of the momentum operator in curvilinear coordinat...The forms of minimum wavepackets (MWPs) corresponding to the geueralized momentum space and coordinates spaca are derived by using the generalized Hermitian expression of the momentum operator in curvilinear coordinates. The several MWPs are discussed according to different upper and lower limits of the usual coordinate componets, and the relevant conclusions are drawn in this paper.展开更多
Photodissociation of HOBr is an important step in the reaction network of the depletion of ozone in stratosphere.Here,we report the first three-dimensional potential energy surfaces for the lowest three singlet states...Photodissociation of HOBr is an important step in the reaction network of the depletion of ozone in stratosphere.Here,we report the first three-dimensional potential energy surfaces for the lowest three singlet states for HOBr,based on high level multi reference configuration interaction calculations.Quantum dynamics calculations are performed with a real wavepacket method,yielding not only absorption spectra but also internal state and angular distributions of the photodissociation fragments.Our results agree quantitatively with the measured total absorption cross sections of HOBr in the ultraviolet region and reproduce well the observed vibrationally cold and rotationally hot OH/OD fragments via photodissociation of HOBr/DOBr at 266 nm.In addition,we predict that the recoil anisotropy parameters for OH/OD are close to the limiting value of a parallel transition,suggesting a rapid dissociation process at 266 nm following an in-plane transition from the ground state(1^1A')to the 21A'state.This is consistent with the experimental conclusion derived from the measured rotational alignment.However,spin and electronic angular momenta need to be taken into account in the future to achieve a more quantitative agreement with experiment.Our work is expected to motivate further experimental investigations for this benchmark system.展开更多
The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation （DNS）. It was found that certain sma...The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation （DNS）. It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance （wavepacket） in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting （T-S） waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.展开更多
A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic non...A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.展开更多
The A-band resonance Raman spectra of thiourea were obtained in water and acetonitrile solution. B3LYP/6-311＋＋G（3df,3pd） and RCIS/6-311＋＋G（3df,3pd） calculations were done to elucidate the ultraviolet electroni...The A-band resonance Raman spectra of thiourea were obtained in water and acetonitrile solution. B3LYP/6-311＋＋G（3df,3pd） and RCIS/6-311＋＋G（3df,3pd） calculations were done to elucidate the ultraviolet electronic transitions, the distorted geometry structure and the saddle point of thiourea in 21A excited state, respectively. The resonance Raman spectra were assigned. The absorption spectrum and resonance Raman intensities were modeled using Heller＇s time-dependent wavepacket approach to resonance Raman scattering. The results indicate that largest change in the displacement takes place with the C--S stretch mode u6 （｜△｜=0.95） and noticeable changes appear in the H5N3H6＋H8N4H7 wag v5 （｜△｜=0.19）, NCN symmetric stretch^-C--S stretch＋N3H6＋H8N4 wag v4 （｜△｜=0.18）, while the moderate intensities of 2-15 and 4-15 are mostly due to the large excited state frequency changes of v15, but not due to its significant change in the normal mode displacement. The mechanism of the appearance of even overtones of the S-CN2 out of plane deformation is explored. The results indicate that a Franck-Condon region saddle point is the driving force for the quadric phonon mechanism within the standard A-term of resonance Raman scattering, which leads to the pyramidalization of the carbon center and the geometry distortion of thiourea molecule in 21A excited state.展开更多
In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arb...In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.展开更多
We have studied the quantum and classical motions of a single Paul trapped ion interacting with a timeperiodic laser field. By using the test-function method, we construct n exact solutions of quantum dynamics that de...We have studied the quantum and classical motions of a single Paul trapped ion interacting with a timeperiodic laser field. By using the test-function method, we construct n exact solutions of quantum dynamics that describe the generalized squeezed coherent states with the expectation orbits being the corresponding classical ones. The spacetime evolutions of the exact probability densities show some wavepacket trains. It is demonstrated analytically that by adjusting the laser intensity and frequency, we can control the center motions of the wavepacket trains. We also discuss the other physical properties such as the expectation value of energy, the widths and heights of the wavepackets, and the resonance loss of stability.展开更多
基金supported by the National Natural Science Foundation of China(Grants 11232011,11402262,11572314,and 11621202)the Fundamental Research Funds for the Central Universitiesthe China Postdoctoral Science Foundation(Grant 2017M610823)
文摘Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at down- stream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.
基金supported by the National Natural Science Foundation of China (Grants 11232011, 11402262, 11572314, 11621202)the Fundamental Research Funds for the Central Universities
文摘A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The modes have high coherence of near-field pressure for both jets, while the coherence of modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12075198, 12247106, and 12247101)。
文摘In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that applies only in the neighborhoods of the lowest two quantum resonances, the proposed theory is applicable in the neighborhoods of all quantum resonances in principle by considering the quantum effect of the free rotation at a quantum resonance. In particular, it is confirmed by simulations that the quantum wavepacket dynamics can be successfully forecasted based on the generalized pseudoclassical dynamics, offering an intriguing example where it is feasible to bridge the dynamics in the deep quantum regime to the classical dynamics. The application of the generalized pseudoclassical theory to the PT-symmetric kicked rotor is also discussed.
文摘Non-spreading nature of Bessel spatiotemporal wavepackets is theoretically and experimentally investigated and orders of magnitude improvement in the spatiotemporal spreading has been demonstrated.The spatiotemporal confinement provided by the Bessel spatiotemporal wavepacket is further exploited to transport transverse orbital angular momentum through embedding spatiotemporal optical vortex into the Bessel spatiotemporal wavepacket, constructing a new type of wavepacket: Bessel spatiotemporal optical vortex. Both numerical and experimental results demonstrate that spatiotemporal vortex structure can be well maintained and confined through much longer propagation. High order spatiotemporal optical vortices can also be better confined in the spatiotemporal domain and prevented from further breaking up, overcoming a potential major obstacle for future applications of spatiotemporal vortex.
基金Project partially supported by the State Key Development Program of Basic Research of China (Grant No 2007CB310405)
文摘This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanica is shown explicitly in the system.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10575034 and 10275023）, and the Science Foundation of the Laboratory of Magnetic Resonance and Atomic and Molecular Physics, China （Grant No T152504）.
文摘We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.
基金Project supported by National Natural Science Foundation of ChinaCentre of Advanced Academic Research of Zhongshan University.
文摘By means of WKB expansions, new fourth order evolution equations are derived for two-dimensional Stokes waves over the bottom with arbitrary depth. The effects of slowly varying depth h= h (ε~2 x) and current U=U(ε~2x, ε~2t, ε~4z) on the evolution of a packet of Stokes waves are considered as well. In addition, numerical simulation is performed for the evolution of single envelope by finite-difference method.
文摘The forms of minimum wavepackets (MWPs) corresponding to the geueralized momentum space and coordinates spaca are derived by using the generalized Hermitian expression of the momentum operator in curvilinear coordinates. The several MWPs are discussed according to different upper and lower limits of the usual coordinate componets, and the relevant conclusions are drawn in this paper.
基金supported by the National Key R&D Program of China (2017YFA0303500)Anhui Initiative in Quantum Information Technologies(AHY090200).
文摘Photodissociation of HOBr is an important step in the reaction network of the depletion of ozone in stratosphere.Here,we report the first three-dimensional potential energy surfaces for the lowest three singlet states for HOBr,based on high level multi reference configuration interaction calculations.Quantum dynamics calculations are performed with a real wavepacket method,yielding not only absorption spectra but also internal state and angular distributions of the photodissociation fragments.Our results agree quantitatively with the measured total absorption cross sections of HOBr in the ultraviolet region and reproduce well the observed vibrationally cold and rotationally hot OH/OD fragments via photodissociation of HOBr/DOBr at 266 nm.In addition,we predict that the recoil anisotropy parameters for OH/OD are close to the limiting value of a parallel transition,suggesting a rapid dissociation process at 266 nm following an in-plane transition from the ground state(1^1A')to the 21A'state.This is consistent with the experimental conclusion derived from the measured rotational alignment.However,spin and electronic angular momenta need to be taken into account in the future to achieve a more quantitative agreement with experiment.Our work is expected to motivate further experimental investigations for this benchmark system.
基金supported by the National Basic Research Program of China (Grant No. 2009CB724103)
文摘The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation （DNS）. It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance （wavepacket） in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting （T-S） waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.
基金supported by the National Natural Science Foundation of China under Grant No.11772341the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB22040203。
文摘A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.
基金This work was supported by the National Natural Science Foundation of China （No.21033002 and No.20803066） and the National Basic Research Program of China （No.2007CB815203）.
文摘The A-band resonance Raman spectra of thiourea were obtained in water and acetonitrile solution. B3LYP/6-311＋＋G（3df,3pd） and RCIS/6-311＋＋G（3df,3pd） calculations were done to elucidate the ultraviolet electronic transitions, the distorted geometry structure and the saddle point of thiourea in 21A excited state, respectively. The resonance Raman spectra were assigned. The absorption spectrum and resonance Raman intensities were modeled using Heller＇s time-dependent wavepacket approach to resonance Raman scattering. The results indicate that largest change in the displacement takes place with the C--S stretch mode u6 （｜△｜=0.95） and noticeable changes appear in the H5N3H6＋H8N4H7 wag v5 （｜△｜=0.19）, NCN symmetric stretch^-C--S stretch＋N3H6＋H8N4 wag v4 （｜△｜=0.18）, while the moderate intensities of 2-15 and 4-15 are mostly due to the large excited state frequency changes of v15, but not due to its significant change in the normal mode displacement. The mechanism of the appearance of even overtones of the S-CN2 out of plane deformation is explored. The results indicate that a Franck-Condon region saddle point is the driving force for the quadric phonon mechanism within the standard A-term of resonance Raman scattering, which leads to the pyramidalization of the carbon center and the geometry distortion of thiourea molecule in 21A excited state.
基金This work was supported by the National Basic Research Program of China （No.2013CB922200）, the National Natural Science Foundation of China （No.21222308, No.21103187, and No.21133006）, the Chinese Academy of Sciences, and the Key Research Program of the Chinese Academy of Sciences.
文摘In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.
基金the National Basic Research Program of China，the National Natural Science Foundation of China，the Chinese Academy of Sciences, and the Key Research Program of Chinese Academy of Sciences
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10575034 and 10275023, and the Laboratory of Magnetic Resonance and Atomic and Molccular Physics of China under Grant No. T152504
文摘We have studied the quantum and classical motions of a single Paul trapped ion interacting with a timeperiodic laser field. By using the test-function method, we construct n exact solutions of quantum dynamics that describe the generalized squeezed coherent states with the expectation orbits being the corresponding classical ones. The spacetime evolutions of the exact probability densities show some wavepacket trains. It is demonstrated analytically that by adjusting the laser intensity and frequency, we can control the center motions of the wavepacket trains. We also discuss the other physical properties such as the expectation value of energy, the widths and heights of the wavepackets, and the resonance loss of stability.
