Two-dimensional Wave Packet Research Articles

Space- and time-resolved Brillouin light scattering from nonlinear spin-wave packets

We have constructed a new Brillouin light scattering apparatus, based on the Sandercock multipass tandem interferometer design, for space- and time-resolved investigations of nonlinear wave packets in thin films. We have applied the method to studies of nonlinear spin-wave pulse propagation in yttrium iron garnet (YIG) films. Spatial resolution is achieved by scanning the laser spot across the YIG film surface, and temporal resolution is obtained by measuring the elapsed time between the launch of spin-wave pulses by an applied microwave pulse and the arrival of the respective inelastically scattered photons at the detector. We report the observation of nonlinear self-focusing of wave beams and pulses in one and two dimensions, the formation of one-dimensional envelope solitons, and of strongly localized, two-dimensional wave packets, ‘spin-wave bullets’, analogous to ‘light bullets’ predicted in nonlinear optics. By generating two counter-propagating wave pulses, pulse collision experiments were performed. We show that quasi-one-dimensional envelope solitons formed in narrow film stripes (‘waveguides’) retain their shapes after collision, while two-dimensional spin-wave packets formed in wide YIG films are destroyed in collision.

Dimensionality effects on transition state resonances for [formula omitted] and [formula omitted] reactive collisions

The transition state resonances of the title reactions have been studied on the accurate double many-body expansion (DMBE) potential energy surface for H3 using two-dimensional (2D) and three-dimensional (3D) time-dependent wave packet propagation methods. It is shown that the resonance energies are strongly associated with the vibrational threshold states of the molecular fragment obtained upon dissociation, both in the 2D and 3D calculations. However, although the two systems have the same threshold states, the resonance widths for the 2D D+HD collisions are found to be considerably narrower than for the 3D ones, while no such phenomenon is observed for H+DH. As a result, we have concluded that there is an apparent dimensional effect on the resonance widths of the heavy–light–heavy (HLH) reaction.

Numerical simulation of electron diffraction through a narrow constriction

We performed time-evolved numerical simulations of a two-dimensional electron wave packet passing through a semicircular constriction (very short quantum wire) by solving the time-dependent Schrödinger equation using the finite difference method to understand the nature of electron diffraction phenomena in semiconductors. By Fourier transformation, we calculated the time-evolved electron wave packet in wave number space, which shows the transition from the Gaussian distribution to the circular distribution having equal energy by entering constriction. The obtained results are compared with the results of our previous simulations of an electron wave packet passing through a rectangular constriction. By analyzing the nature of diffracted subpeaks, the following results were obtained: (1) The intensity of the subpeaks diffracted by a semicircular constriction is higher than that by a rectangular one. (2) The starting point of the diffracted subpeaks is the center position of the narrowest width in a constriction, while that for rectangular ones is the center of the constriction entrance. (3) The lateral wave number of the diffracted subpeak increases with the number n, n being the number counted from the main (0th) peak which propagates straight through, although it deviates negatively from the linear relationship obtained for rectangular ones with an increase in n. (4) There is a time delay in the diffracted subpeaks similar to that for rectangular constrictions. The differences between passing through a semicircular constriction and a rectangular one were interpreted as caused by the reflection on the inside wall of the constriction and the energy spread of each quantum level.

Accurate nonadiabatic couplings for H3: Application to predissociation

We report the results of an ab initio calculation, using analytic techniques, of nonadiabatic couplings for H3 between the degenerate 2E′ ground state and the 2s(2A1′), 3s(2A1′) and 3p(2E′) Rydberg states. The calculations employed extensive correlated wave functions that accurately reproduced the energy levels of these states. We have used these couplings as input to a two-dimensional wave packet calculation of dissociation dynamics in order to predict the predissociation lifetimes and final state vibrational distributions produced by the predissociation. A significant isotope effect is found in the final vibrational distributions produced from H3 and D3 predissociation.

Photodissociation of gas phase I3− using femtosecond photoelectron spectroscopy

The photodissociation dynamics of gas phase I3− following 390 nm excitation are studied using femtosecond photoelectron spectroscopy. Both I− and I2− photofragments are observed; the I2− exhibits coherent oscillations with a period of 550 fs corresponding to ∼0.70 eV of vibrational excitation. The oscillations dephase by 4 ps and rephase at 45 and 90.5 ps on the anharmonic I2− potential. The gas phase frequency of ground state I3− is determined from oscillations in the photoelectron spectrum induced by resonance impulsive stimulated Raman scattering. The dynamics of this reaction are modeled using one- and two-dimensional wave packet simulations from which we attribute the formation of I− to three-body dissociation along the symmetric stretching coordinate of the excited anion potential. The photodissociation dynamics of gas phase I3− differ considerably from those observed previously in solution both in terms of the I2− vibrational distribution and the production of I−.

Collisions of Spin Wave Envelope Solitons and Self-Focused Spin Wave Packets in Yttrium Iron Garnet Films

Head-on collisions between two-dimensional self-focused spin wave packets and between quasi-one-dimensional spin wave envelope solitons have been directly observed for the first time in yttrium irongarnet (YIG) films by means of a space- and time-resolved Brillouin light scattering technique. Weshow that quasi-one-dimensional envelope solitons formed in narrow film strips (“waveguides”) retaintheir shapes after collision, while the two-dimensional self-focused spin wave packets formed in wideYIG films are destroyed in collision. [S0031-9007(99)09216-9]

Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space- and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. The experimental results are in good qualitative agreement with numerical simulations.

Quantum-mechanical wave packet calculation of photoinduced surface reaction: O2/Pt(111)

We present a two-dimensional quantum-mechanical wave packet study of photoinduced reaction of O2 on Pt(111) within a mechanism of hot electron/hole excitation of a molecular resonance. Based on three constructed potential energy surfaces including the molecule-surface and intra-molecular coordinates, photoexcitation is simulated by nonadiabatic electronic transitions between the ground state (the chemisorbed O2−) and a negative ion resonance state (the O22− shape resonance) or a neutral O2 state. The wave packet dynamics exhibits a fast energy exchange between the two bonds, giving a comparable yield for desorption and dissociation. The calculated branching ratio, BR=0.5–1.0, between desorption and dissociation and the mean kinetic energy of the desorbed molecules 〈Ekin〉/2kB= 990 K are comparable with the reported experimental data measured in desorption by nanosecond laser pulses, while the vibrational temperature is first predicted by this calculation. In addition our results indicate the importance of a proper treatment of damping effect in a coherent wave packet after deexcitation.

Two-dimensional wave packet studies of photon-stimulated desorption of NO from a metal surface induced by single and multiple electronic excitations

The photon-stimulated desorption dynamics of nitric oxide (NO) from the Pt(111) surface is investigated using time-dependent quantum mechanics. Empirical potential energy surfaces with two degrees of freedom (desorption and NO vibration) are employed for both the neutral and anionic states. The influence of the time delay between transitions is investigated for desorption with single and double excitation/deexcitation cycles. An improved Monte Carlo sampling scheme is proposed for processes undergoing multiple excitations. For desorption involving a single excitation, the calculated vibrational and kinetic energy distributions of the desorbed NO agree very well with experimental observations. When desorption is driven by multiple excitations, higher vibrational excitation is found for NO.

The formation of non-linear waveguides in the resonant interaction of three surface waves

The resonant interaction of three two-dimensional wave packets of capillary and flexural-gravitational waves on the surface of an infinitely deep ideal liquid is investigated. Universal asymptotic equations are obtained using the Hamiltonian approach. The main types of decaying interactions are determined as a function of the group velocities of the wave packets. New exact waveguide-type solutions of the equations describing the interaction between three waves are obtained and investigated taking dispersion into account. By reducing the dynamical system to a central manifold it is proved that a wide class of solutions of the waveguide type exists, which depend on five arbitrary constants. It is proved that they are stable with respect to slow changes in the waveguide boundaries and in the amplitudes of the waves propagating along it.

Interfacial stability and nonlinear properties of electrohydrodynamics

A weakly nonlinear evolution of two-dimensional wave packets on the surface of a fluid layer in the presence of an applied electric field is investigated. The method used is that of multiple scales. Two nonlinear Schrödinger equations describing the perturbed system are obtained, one of which leads to the determination of the cutoff electric field. The other Schrödinger equation is used to analyze the stability of the system.

Direct subsurface absorption of hydrogen on Pd(111)

We summarize and discuss some of the available experimental and theoretical data important for understanding the role played by subsurface sites in dissociative chemisorption calculations for the H2/Pd(111) system. Then we use a semi-empirical potential energy surface (PES) to model the interaction of a H2 molecule impinging on a Pd(111) surface. The London–Eyring–Polanyi–Sato (LEPS) construction has been extended to make direct subsurface absorption possible. A two-dimensional wave packet calculation is used to find qualitative trends in the direct subsurface absorption and to reveal the time scales involved. We suggest that a partial in-plane relaxation occurs for the slowest incoming particles, thus resulting in a higher direct subsurface absorption probability for low energies.

Dissociation and atom recombination of H2 and D2 on metallic surfaces: A theoretical survey

Abstract

Wave packets, resonant interactions and soliton formation in inlet pipe flow

The development of disturbances (two-dimensional non-linear and three-dimensional linear) in the entrance region of a circular pipe is studied in the limit of Reynolds numberR→ ∞ in the framework of triple-deck theory. It is found that lower-branch axisymmetric disturbances can interact in the resonant manner. Numerical calculations show that a two-dimensional nonlinear wave packet grows much more rapidly than that in the boundary layer on a flat plate, producing a spike-like solution which seems to become singular at a finite time. Large-sized, short-scaled disturbances are also studied. In this case the development of axisymmetric disturbances is governed by single one-dimensional equation in the form of the Korteweg-de Vries and Benjamin-Ono equations in the long- and short-wave limits respectively. The nonlinear interactions of these disturbances lead to the formation of solitons which can run both upstream and downstream. Linear three-dimensional wave packets are also calculated.

Time-evolved numerical simulation of a two-dimensional electron wave packet through a quantum point contact

We performed time-evolved numerical simulation of a two-dimensional electron wave packet through a quantum point contact using the finite difference method to simulate the diffraction phenomenon of a single electron. We found that the transmitted wave packet has diffracted subpeaks which show the following properties: (1) The traces of diffracted subpeaks start from the center of the slit entrance. (2) Lateral wave number of diffracted subpeaks is quantized. (3) The diffraction angles are determined by slit width and the initial electron wave packet energy. (4) The number of allowed diffracted subpeaks is determined by potential barrier thickness. (5) There is a delay in the motion of diffracted subpeaks due to quantization inside the slit.

A quantum mechanical, time-dependent wave packet interpretation of the diffuse structures in the S→S1 absorption spectrum of FNO: Coexistence of direct and indirect dissociation

We have investigated the photodissociation of FNO in the first absorption band (S0→S1) by a two-dimensional wave packet study based on an ab initio potential energy surface. The quantum chemical calculations were performed in the multiconfiguration self-consistent field (MCSCF) approach including the N–O and the F–NO bond distances with the FNO bond angle being fixed. The most striking feature of the time-dependent dynamical analysis is a bifurcation of the wave packet near the Franck–Condon point: while one part of the wave packet leaves the inner region of the potential energy surface very rapidly, a second part remains trapped for several periods in an extremely shallow well at short F–NO distances. The direct part leads to a broad background in the absorption spectrum while the trapped portion of the wave packet gives rise to relatively narrow resonances, i.e., well resolved diffuse vibrational structures. The bandwidth decreases with the degree of internal excitation. The calculated spectrum agrees well with the measured one.

Collision-induced energy transfer in p-difluorobenzene by light atoms: a wave-packet scattering calculation

The collisional excitation and relaxation of para-difluorobenzene ( p-DFB) by light atoms have been studied by a wave-packet scattering method. In our model the light atom is represented by a two-dimensional wave packet and the vibrations of p-DFB molecule are treated classically. We found that the v 30 mode, which is the mode with the lowest vibrational frequency and one which involves an out-of-plane motion of the fluorine atoms, is most easily excited or relaxed in the collisions. This is in agreement with the experimental and other theoretical results. This study shows that this combined trajectory/wave-packet approach can be used to treat intermolecular energy transfer in collisions of atoms with polyatomic molecules.

Dynamics of two-dimensional solitons in weakly dispersive media

Formation, evolution and interaction of two-dimensional solitons and wave packets in weakly dispersive and dissipative media is studied numerically. The master equation is a hybrid of the Zabolotskaya-Khokhlov and Kadomtsev-Petviashvili equations with a Kawahara term.

Dynamic simulation of two-dimensional wave packets and superposition

A simulation study of a neutron interferometer of Si is carried out. How a wave packet is decomposed into two using the Bragg diffraction was already reported. This paper describes how the divided two parts of a single-neutron wave packet are again superposed. In order for wave packets to be superposed both must belong to the same Hilbert space and a certain physical process to superpose them is necessary. In an interferometer atomic potentials of Si play this role.

Dynamic simulation of two-dimensional wave packets and virtual states

In studying the dynamical diffraction effect of neutrons it has been clarified that eigenstates of a quantum system composed of periodic potentials with free spaces on both ends play a crucial role in determining the Bragg reflection, rocking curves, Pendellösung effect, and so on. These eigenstates can be called virtual states, since the occupancy probability within the potential region is significantly modified by the existing potential, even though the energies of concern are much larger than the potential barrier heights.