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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

New Approach to Study the Evolution of Rossby Wave Packet

The average variational principle was employed in this paper to study the evolution of large-scale and slowly varying Rossby wave packet with basic flow both in barotropic and baroclinic atmospheres. The evolution of the structure of Rossby wave packet with both time and space was studied. The results obtained in this paper are similar to the results of by WKBJ method. In addition, the dispersive process of the wave packet was analysed by taking Gaussian type wave packet as an initial disturbance. The valid time scale for application of wave packet theory in the atmosphere was obtained.

Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities

Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.

The Quantum Oscillatory Modulated Potential—Electric Field Wave Packets Produced by Electrons

In this work we are formulating a new theory for describing the waving nature of a microscopic electric particle. Based on the predictions of the Quantum Oscillatory Modulated Potential—QOMP, for describing the interaction between two microscopic electric particles, electron-electron, for instance, we are postulating that the waving behavior of these particles may be an attribute of the charges of the particles and not their masses as currently accepted. For a microscopic electric charge, we are presenting new arguments showing that the electric field in the vicinity of a microscopic charge is spatially waving and can be determined as the gradient per unit of charge of this new quantum interaction potential, with use of an appropriated phase factor to account for the behavior of an unbound electron. Differently of what is predicted by the classical Coulomb electric field, when a charged particle is moving under the action of a potential of V volts, the new electric field existing around the charge has the form of a wave packet. For typical values of the potential V, the wavelength of the waving electric field is in very good agreement with those experimentally observed with diffraction of electrons in crystalline solids.

The Stable Wave Packet and Uncertainty

The traveling wave group that is defined on conserved physical values is the vehicle of transmission for a unidirectional photon or free particle having a wide wave front. As a stable wave packet, it expresses internal periodicity combined with group localization. An uncertainty principle is precisely derived that differs from Heisenberg’s. Also derived is the phase velocity beyond the horizon set by the speed of light. In this space occurs the reduction of the wave packet which is represented by comparing phase velocities in the direction of propagation with the transverse plane. The new description of the wave function for the stable free particle or antiparticle contains variables that were previously ignored. Deterministic physics must always appear probabilistic when hidden variables are bypassed. Secondary hidden variables always occur in measurement. The wave group turns out to be both uncertain and probabilistic. It is ubiquitous in physics and has many consequences.

The Stable Wave Packet in the Foundations of Quantum Mechanics

The stable wave packet has been missing in quantum mechanics for a long time. A consistent argument finds, in antimatter, regular group and phase velocities, along with negative energy and negative mass. For this, a new wave function is derived for free antiparticles, consistent with the Feynman-Stueckelberg switching principle. The wave packet, expressing internal periodicity together with external confinement, is ubiquitous in physics. The stable wave packet has many consequences, a few of which are mentioned. They extend to the debate about what is measurable in physics and to localization of quantized properties in entangled particles.