The Propagation of Wave Packets and Its Relationship with the Subtropical Jet over Southern China in January 2008

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.

Interference of dissociating wave packets in the I_2 molecule driven by femtosecond laser pulses

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.

Propagation of General Wave Packets in Some Classical and Quantum Systems

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.

Channel-resolved subcycle interferences of electron wave packets emitted from H_(2) in two-color laser fields

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.

Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

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.

Theoretical study of the influence of intense femtosecond laser field on the evolution of the wave packet and the population of NaRb molecule

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.

Influence of laser fields on the vibrational population of molecules and its wave-packet dynamical investigation

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.

A numerical study on the generation of a distinct type of nonlinear internal wave packet in the South China Sea

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.

Time-dependent Wave Packet Quantum Scattering Study of Reaction S（3p）＋H2→HS＋H on a New ab initio Potential Energy Surface 3A’

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.

Study on wave packet dynamics of E^1Σ_g^+ state of Li_2 with femtosecond-resolved photoelectron spectra

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.

The Relationship Between Abnormal Meiyu and Medium-Term Scale Wave Perturbation Energy Propagation Along the East Asian Subtropical Westerly Jet

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.

Large-scale edge waves generated by a moving atmospheric pressure

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.

Time-Dependent Quantum Wave Packet Calculation for Reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S) on Ab Initio Potential Energy Surface

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.

Selective excitation of the molecular rotational wave packet by two time-delayed laser pulses

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.

Isolated attosecond electron wave packet diffraction

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.

Delay time dependence of wave packet motion and population transfer of four-level K_2 molecule in pump–pump–probe pulses

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.

High-Accurate Transparent Boundary Conditions for Time-Dependent Quantum Wave Packet Method

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.

Dynamics of the Au+H2 reaction by time-dependent wave packet and quasi-classical trajectory methods

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.

Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave

We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave, and particularly calculate the atomic inversion of the wave packet. A general method of calculation is presented. The results are interesting. For example, if the wave packet is very narrow or/and the interaction is very strong, no matter the atom is initially in its ground state or excited state, the atomic inversion approaches zero as time approaches infinity. If the atom is initially in its ground state and excited state with the probability 1/2 respectively, and if the momentum density is an even function, then the atomic inversion equals zero at any time.

Equivalence of String Classical and Quantum Energy beside Equivalence of Wave Packet and Relativistic Velocity in Eucleadian and Curved Space

Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.