Non-diffractive space-time wave packets(nSTWPs) represent a broad class of optical pulses capable of propagating without diffraction or dispersion in linear media. In this work, we introduce a complete family of nSTWP...Non-diffractive space-time wave packets(nSTWPs) represent a broad class of optical pulses capable of propagating without diffraction or dispersion in linear media. In this work, we introduce a complete family of nSTWPs that remain invariant under transverse Lorentz boosts. The Lorentz-invariant behavior of these STWPs is rigorously analyzed through their associated spectral line function, providing new insights into their fundamental properties. Furthermore, we quantify the limitations of this invariance and compare the robustness of the proposed nSTWPs against conventional nSTWPs.展开更多
The propagation of wave packets and its relationship with the subtropical jet was investigated for the period 26 29 January 2008 over southern China using ECMWF Interim re-analysis data. Wave packets propagated from t...The propagation of wave packets and its relationship with the subtropical jet was investigated for the period 26 29 January 2008 over southern China using ECMWF Interim re-analysis data. Wave packets propagated from the north to the south side of an upper front with eastward development along the upper front during this period. Due to the eastward development of propagation, the acceleration of geostrophic westerly winds shifted eastward along the front. There were two primary sources of the propagation of wave packets at around 30°N. The first was the temperature inversion layer below 500 hPa, and the second was baroclinic zones located along the polarward flank of the subtropical jet in the middle and upper troposphere. Most wave packets propagated horizontally from the baroclinic zones and then converged on the zero meridional gradients of zonal winds.展开更多
The interference between two dissociating wave packets of the I2 molecule driven by femtosecond laser pulses is theoreticaly studied by using the time-dependent quantum wave packet method. Both the internuclear distan...The interference between two dissociating wave packets of the I2 molecule driven by femtosecond laser pulses is theoreticaly studied by using the time-dependent quantum wave packet method. Both the internuclear distance-and velocity-dependent density functions are calculated and discussed. It is demonstrated that the interference pattern is determined by the phase difference and the delay time between two pump pulses. With two identical pulses with a delay time of 305 fs and a FWHM of 20 fs, more interference fringes can be observed, while with two pump pulses with a delay time of 80 fs and a FWHM of 20 fs, only a few interference fringes can be observed.展开更多
In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no p...In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group Velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.展开更多
We report on the observation of subcycle interferences of electron wave packets released during strong field ionization of H_2 with cycle-shaped two-color laser fields. With a reaction microscope we measure three-dime...We report on the observation of subcycle interferences of electron wave packets released during strong field ionization of H_2 with cycle-shaped two-color laser fields. With a reaction microscope we measure three-dimensional momentum distributions of photoelectrons correlated with either H_2^+ or protons within different energy ranges generated by dissociation of H_2^+. We refer to these different types of photoelectrons as channels. Our results show that the subcycle interference structures of electron wave packets are very sensitive to the cycle shape of the two-color laser field. We explain this behavior by the dependence of the ionization time within an optical cycle on the shape of the laser field cycle. The subcycle interference structures can be further used to obtain insight into the subcycle dynamics of molecules during strong field interaction.展开更多
From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and...From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.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
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
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
A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Exper...A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Experiment in 2001. Data analysis shows that the occurrence of the distinct internal wave packet is closely related with the occurrence of lower-high internal tides; the internal tides are mixed in the experimental area and, thus, there is diurnal inequality between the heights of two neighboring internal tides. Modeling of internal tides and internal solitary waves in a shoaling situation suggests that this type of wave packet can be generated in the South China Sea by the large shoaling of internal solitary waves and internal tides. Both the internal solitary waves and the internal tides come from the direction of Luzon Strait. The initial large internal solitary waves contribute to the occurrence of the largest internal solitary wave in the middle of the packet and the waves behind the largest intemal solitary wave, while the shoaling internal tides bring about the nonlinear internal waves in front of the largest internal solitary wave via interaction with the local shelf topography.展开更多
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
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
The East Asian subtropical westerly jet(EASWJ)is one of the most important factors modulating the Meiyu rainfall in the Yangtze-Huaihe River Basin,China.This article analyzed periods of the medium-term EASWJ variation...The East Asian subtropical westerly jet(EASWJ)is one of the most important factors modulating the Meiyu rainfall in the Yangtze-Huaihe River Basin,China.This article analyzed periods of the medium-term EASWJ variation,wave packet distribution and energy propagation of Rossby waves along the EASWJ during Meiyu season,and investigated their possible influence on abnormal Meiyu rain.The results showed that during the medium-term scale atmospheric dynamic process,the evolution of the EASWJ in Meiyu season was mainly characterized by the changes of3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves.The strong perturbation wave packet and energy propagation of the 3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves are mostly concentrated in the East Asian region of 90°-150°E,where the two wave trains of perturbation wave packets and wave-activity flux divergence coexist in zonal and meridional directions,and converge on the EASWJ.Besides,the wave trains of perturbation wave packet and wave-activity flux divergence in wet Meiyu years are more systematically westward than those in dry Meiyu years,and they are shown in the inverse phases between each other.In wet(dry)Meiyu year,the perturbation wave packet high-value area of the 10-15 d low-frequency variability is located between the Aral Sea and the Lake Balkhash(in the northeastern part of China),while over eastern China the wave-activity flux is convergent and strong(divergent and weak),and the high-level jets are strong and southward(weak and northward).Because of the coupling of high and low level atmosphere and high-level strong(weak)divergence on the south side of the jet over the Yangtze-Huaihe River Basin,the low-level southwest wind and vertically ascending motion are strengthened(weakened),which is(is not)conducive to precipitation increase in the Yangtze-Huaihe River Basin.These findings would help to better understand the impact mechanisms of the EASWJ activities on abnormal Meiyu from the perspective of medium-term scale Rossby wave energy propagation.展开更多
Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only ...Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.展开更多
The blades on the plane are one of the most important parts of the engine,in the course of service,due to high temperature,strong vibration and great centrifugal force and so on.The using environment is very bad,so it...The blades on the plane are one of the most important parts of the engine,in the course of service,due to high temperature,strong vibration and great centrifugal force and so on.The using environment is very bad,so it is easy to produce fatigue cracks in the welding site and the near surface of the root,which will seriously affect the blade of the work intensity and fatigue life,and even the safety of aircraft structure,causing a huge security risk.Therefore,it must be tested.In order to solve the problem of the rapid detection of aircraft engine in situ cracks,and gett the rela-tionship between feature information and detect depth,the laboratory experimental platform was built,laser was used to excite laser ultrasonic signals on a range of aviation aluminum plates with different depth defects,the collected sig-nal was processed by wavelet de-noising,and the band energy distribution of the reflected echo signal was studied by using wavelet packet.The results show that the energy of reflected echo signal is mainly concentrated in the S80~So7 band.When the depth of defect is 0.2 mm to 0.4 mm,the energy is mainly concentrated in the adjacent bands.When the depth of defect is 0.5 mm to 0.7 mm,the energy is mainly concentrated in the two bands.This method provides a way to quantify surface micro-defects by ultrasonic signals,which will lay a foundation for the future analysis of crack depth from band energy.In order to avoid the interference of other irregular cracks,the cracks of the aviation aluminum parts are used as ar-tificial way for producing.The overall size of the specimen is 200 mmx80 mmx100 mm,the width of the defect is 0.15 mm,the range of the defect depth is 0.2 mm~0.7 mm,step size is 0.1 mm,and the total number of the specimen is six.After the experimental data is proposed,choosing the reflected echo signal for analysis,performing wavelet packet transform,the decomposition layer is 8.The percentage in the Sao~Sa7band is 89.77%、91.82%、91.41%、90.94%、90.19%、and 87.86%.The result shows that most of the energy is concentrated in the first eight bands.Therefore,the paper selects the first eight bands for analysis.In order to analyze the distribution characteristics of the different depth defect and the band energy,the energy dis-tribution of the first four bands of the defect depth of 0.2 mm to 0.4 mm is plotted in Fig,according to the spectrum,getting the center frequency were 3.14 MHz,2.58 MHz,2.17 MHz.These frequencies are located in the S83,S82,S82 band,respectively,which are the largest energy band,but the energy distribution in the adjacent segment Ss:also ac-counts for a larger proportion.When the depth of the defect increases from 0.2 mm to 0.4 mm,the center frequency decreases gradually,and the sum of the energy of the center frequency band and the adjacent higher energy band in-creases gradually.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
In this paper, we investigate the control of the molecular wave packet of a linear molecule by two femtosecond laser pulses. It is shown that the odd and the even rotational wave packets created by a single laser puls...In this paper, we investigate the control of the molecular wave packet of a linear molecule by two femtosecond laser pulses. It is shown that the odd and the even rotational wave packets created by a single laser pulse can be selectively excited by accurately controlling the time delay of another laser pulse. By inserting the peak of the second laser pulse at the position of maximum or minimum value around quarter or three quarter rotational period of the slope curve with odd （or even） rotational wave packet contribution that is created by the first laser pulse, the odd rotational wave packet can be enhanced （or suppressed） while the even rotational wave packet is suppressed （or enhanced）. As a result, the molecular alignments around quarter and three quarter rotational periods can be obtained. Moreover, it is also shown that by inserting the second laser pulse around the quarter or three quarter rotational periods, the changes in the maximum degree of the molecular alignment for the odd and the even rotational wave packet contributions are consistent with their corresponding slope curves at these positions.展开更多
Wave-particle duality is one of the most fundamental and mysterious natures of matters. Here, we present an interesting scheme of isolated electron wave packet diffraction with a few-cycle laser pulse and an extreme u...Wave-particle duality is one of the most fundamental and mysterious natures of matters. Here, we present an interesting scheme of isolated electron wave packet diffraction with a few-cycle laser pulse and an extreme ultraviolet （XUV） pulse. The diffraction fringes are clearly present in the laser dressed XUV photoelectron spectra, strongly resembling the Airy diffraction pattern of optical waves. This phenomenon suggests a great potential of attosecond diffractometry. According to this scheme we also propose a simple method to determine the XUV pulse duration from the photoelectron spectra with a rather high resolution.展开更多
The effect of delay time on photoelectron spectra and state populations of a four-level ladder K2 molecule is investigated by a pump1–pump2–probe pulse via the time-dependent wave packet approach. The periodical mot...The effect of delay time on photoelectron spectra and state populations of a four-level ladder K2 molecule is investigated by a pump1–pump2–probe pulse via the time-dependent wave packet approach. The periodical motion of the wave packet leads to the periodical change of the photoelectron spectra. The Autler–Townes triple splitting appears at zero delay time, double splitting appears at nonzero delay time between pump1 and pump2 pulses, and no splitting appears at nonzero delay time between pump2 and probe pulses. The periodical change of the state populations with the delay time may be due to the coupling effect between the two pulses. It is found that the selectivity of the state populations may be attained by regulating the delay time. The results can provide an important basis for realizing the optical control of molecules experimentally.展开更多
文摘Non-diffractive space-time wave packets(nSTWPs) represent a broad class of optical pulses capable of propagating without diffraction or dispersion in linear media. In this work, we introduce a complete family of nSTWPs that remain invariant under transverse Lorentz boosts. The Lorentz-invariant behavior of these STWPs is rigorously analyzed through their associated spectral line function, providing new insights into their fundamental properties. Furthermore, we quantify the limitations of this invariance and compare the robustness of the proposed nSTWPs against conventional nSTWPs.
基金supported by the National Natural Science Foundation of China (Grant Nos. 40930950 and 40921160379)the Chinese Academy of Meteorological Sciences State Key Laboratory of Severe Weather (LaSW+1 种基金Grant No. 2011LASW-A01)the National Basic Research Project of China under Grant No. 2012CB417201
文摘The propagation of wave packets and its relationship with the subtropical jet was investigated for the period 26 29 January 2008 over southern China using ECMWF Interim re-analysis data. Wave packets propagated from the north to the south side of an upper front with eastward development along the upper front during this period. Due to the eastward development of propagation, the acceleration of geostrophic westerly winds shifted eastward along the front. There were two primary sources of the propagation of wave packets at around 30°N. The first was the temperature inversion layer below 500 hPa, and the second was baroclinic zones located along the polarward flank of the subtropical jet in the middle and upper troposphere. Most wave packets propagated horizontally from the baroclinic zones and then converged on the zero meridional gradients of zonal winds.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10674022 and 20633070)
文摘The interference between two dissociating wave packets of the I2 molecule driven by femtosecond laser pulses is theoreticaly studied by using the time-dependent quantum wave packet method. Both the internuclear distance-and velocity-dependent density functions are calculated and discussed. It is demonstrated that the interference pattern is determined by the phase difference and the delay time between two pump pulses. With two identical pulses with a delay time of 305 fs and a FWHM of 20 fs, more interference fringes can be observed, while with two pump pulses with a delay time of 80 fs and a FWHM of 20 fs, only a few interference fringes can be observed.
基金The project supported by National Natural Science Foundation of China under Grant No. 10275098The author is grateful to professor Nai-Ben Huang for useful discussions.
文摘In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group Velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.
基金financed by the Austrian Science Fund(FWF)under grants P25615-N27,P28475-N27,P21463N22,P27491-N27 and SFB-F49 NEXTliteby a starting grant from the European Research Council(ERC project CyFi)
文摘We report on the observation of subcycle interferences of electron wave packets released during strong field ionization of H_2 with cycle-shaped two-color laser fields. With a reaction microscope we measure three-dimensional momentum distributions of photoelectrons correlated with either H_2^+ or protons within different energy ranges generated by dissociation of H_2^+. We refer to these different types of photoelectrons as channels. Our results show that the subcycle interference structures of electron wave packets are very sensitive to the cycle shape of the two-color laser field. We explain this behavior by the dependence of the ionization time within an optical cycle on the shape of the laser field cycle. The subcycle interference structures can be further used to obtain insight into the subcycle dynamics of molecules during strong field interaction.
文摘From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.
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Supported by the National Basic Research Program of China (973 Program, No. 2007CB416605)the Office of Naval Research (ONR) (No. N00014-03-0337)+1 种基金the National Aeronautics and Space Administration (No. NAG5-11773)the National Oceanic and Atmospheric Administration (No. NA17EC2449)
文摘A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Experiment in 2001. Data analysis shows that the occurrence of the distinct internal wave packet is closely related with the occurrence of lower-high internal tides; the internal tides are mixed in the experimental area and, thus, there is diurnal inequality between the heights of two neighboring internal tides. Modeling of internal tides and internal solitary waves in a shoaling situation suggests that this type of wave packet can be generated in the South China Sea by the large shoaling of internal solitary waves and internal tides. Both the internal solitary waves and the internal tides come from the direction of Luzon Strait. The initial large internal solitary waves contribute to the occurrence of the largest internal solitary wave in the middle of the packet and the waves behind the largest intemal solitary wave, while the shoaling internal tides bring about the nonlinear internal waves in front of the largest internal solitary wave via interaction with the local shelf topography.
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.
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.
基金National Natural Science Foundation of China(41575066)National Science and Technology Support Program of China(2015BAC03B04)
文摘The East Asian subtropical westerly jet(EASWJ)is one of the most important factors modulating the Meiyu rainfall in the Yangtze-Huaihe River Basin,China.This article analyzed periods of the medium-term EASWJ variation,wave packet distribution and energy propagation of Rossby waves along the EASWJ during Meiyu season,and investigated their possible influence on abnormal Meiyu rain.The results showed that during the medium-term scale atmospheric dynamic process,the evolution of the EASWJ in Meiyu season was mainly characterized by the changes of3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves.The strong perturbation wave packet and energy propagation of the 3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves are mostly concentrated in the East Asian region of 90°-150°E,where the two wave trains of perturbation wave packets and wave-activity flux divergence coexist in zonal and meridional directions,and converge on the EASWJ.Besides,the wave trains of perturbation wave packet and wave-activity flux divergence in wet Meiyu years are more systematically westward than those in dry Meiyu years,and they are shown in the inverse phases between each other.In wet(dry)Meiyu year,the perturbation wave packet high-value area of the 10-15 d low-frequency variability is located between the Aral Sea and the Lake Balkhash(in the northeastern part of China),while over eastern China the wave-activity flux is convergent and strong(divergent and weak),and the high-level jets are strong and southward(weak and northward).Because of the coupling of high and low level atmosphere and high-level strong(weak)divergence on the south side of the jet over the Yangtze-Huaihe River Basin,the low-level southwest wind and vertically ascending motion are strengthened(weakened),which is(is not)conducive to precipitation increase in the Yangtze-Huaihe River Basin.These findings would help to better understand the impact mechanisms of the EASWJ activities on abnormal Meiyu from the perspective of medium-term scale Rossby wave energy propagation.
基金supported by an NSF grant to Cornell University,the China Scholarship Council and a Korean government MLTMA grant Development of Korea Operational Oceanographic System (KOOS) to KORDI
文摘Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.
文摘The blades on the plane are one of the most important parts of the engine,in the course of service,due to high temperature,strong vibration and great centrifugal force and so on.The using environment is very bad,so it is easy to produce fatigue cracks in the welding site and the near surface of the root,which will seriously affect the blade of the work intensity and fatigue life,and even the safety of aircraft structure,causing a huge security risk.Therefore,it must be tested.In order to solve the problem of the rapid detection of aircraft engine in situ cracks,and gett the rela-tionship between feature information and detect depth,the laboratory experimental platform was built,laser was used to excite laser ultrasonic signals on a range of aviation aluminum plates with different depth defects,the collected sig-nal was processed by wavelet de-noising,and the band energy distribution of the reflected echo signal was studied by using wavelet packet.The results show that the energy of reflected echo signal is mainly concentrated in the S80~So7 band.When the depth of defect is 0.2 mm to 0.4 mm,the energy is mainly concentrated in the adjacent bands.When the depth of defect is 0.5 mm to 0.7 mm,the energy is mainly concentrated in the two bands.This method provides a way to quantify surface micro-defects by ultrasonic signals,which will lay a foundation for the future analysis of crack depth from band energy.In order to avoid the interference of other irregular cracks,the cracks of the aviation aluminum parts are used as ar-tificial way for producing.The overall size of the specimen is 200 mmx80 mmx100 mm,the width of the defect is 0.15 mm,the range of the defect depth is 0.2 mm~0.7 mm,step size is 0.1 mm,and the total number of the specimen is six.After the experimental data is proposed,choosing the reflected echo signal for analysis,performing wavelet packet transform,the decomposition layer is 8.The percentage in the Sao~Sa7band is 89.77%、91.82%、91.41%、90.94%、90.19%、and 87.86%.The result shows that most of the energy is concentrated in the first eight bands.Therefore,the paper selects the first eight bands for analysis.In order to analyze the distribution characteristics of the different depth defect and the band energy,the energy dis-tribution of the first four bands of the defect depth of 0.2 mm to 0.4 mm is plotted in Fig,according to the spectrum,getting the center frequency were 3.14 MHz,2.58 MHz,2.17 MHz.These frequencies are located in the S83,S82,S82 band,respectively,which are the largest energy band,but the energy distribution in the adjacent segment Ss:also ac-counts for a larger proportion.When the depth of the defect increases from 0.2 mm to 0.4 mm,the center frequency decreases gradually,and the sum of the energy of the center frequency band and the adjacent higher energy band in-creases gradually.
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Project supported by the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2008183)the Open Research Fund of State Key Laboratory of Precision Spectroscopy,East China Normal University
文摘In this paper, we investigate the control of the molecular wave packet of a linear molecule by two femtosecond laser pulses. It is shown that the odd and the even rotational wave packets created by a single laser pulse can be selectively excited by accurately controlling the time delay of another laser pulse. By inserting the peak of the second laser pulse at the position of maximum or minimum value around quarter or three quarter rotational period of the slope curve with odd （or even） rotational wave packet contribution that is created by the first laser pulse, the odd rotational wave packet can be enhanced （or suppressed） while the even rotational wave packet is suppressed （or enhanced）. As a result, the molecular alignments around quarter and three quarter rotational periods can be obtained. Moreover, it is also shown that by inserting the second laser pulse around the quarter or three quarter rotational periods, the changes in the maximum degree of the molecular alignment for the odd and the even rotational wave packet contributions are consistent with their corresponding slope curves at these positions.
基金Project supported by the National Natural Science Foundation of China (Grant No.11005088)the Basic and Advanced Technology of Henan Province of China (Grant No.102300410241)the Scientific Research Foundation of Education Department of Henan Province of China (Grant Nos.2009A140006 and 20116140018)
文摘Wave-particle duality is one of the most fundamental and mysterious natures of matters. Here, we present an interesting scheme of isolated electron wave packet diffraction with a few-cycle laser pulse and an extreme ultraviolet （XUV） pulse. The diffraction fringes are clearly present in the laser dressed XUV photoelectron spectra, strongly resembling the Airy diffraction pattern of optical waves. This phenomenon suggests a great potential of attosecond diffractometry. According to this scheme we also propose a simple method to determine the XUV pulse duration from the photoelectron spectra with a rather high resolution.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11704178 and 11764041)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.15B204)
文摘The effect of delay time on photoelectron spectra and state populations of a four-level ladder K2 molecule is investigated by a pump1–pump2–probe pulse via the time-dependent wave packet approach. The periodical motion of the wave packet leads to the periodical change of the photoelectron spectra. The Autler–Townes triple splitting appears at zero delay time, double splitting appears at nonzero delay time between pump1 and pump2 pulses, and no splitting appears at nonzero delay time between pump2 and probe pulses. The periodical change of the state populations with the delay time may be due to the coupling effect between the two pulses. It is found that the selectivity of the state populations may be attained by regulating the delay time. The results can provide an important basis for realizing the optical control of molecules experimentally.
