Wave Packets Propagation in the Subwavelength Regime Near the Dirac Point

Observational studies show that the main energy source for developing cyclones is due to downstream radiation from existing upstream disturbances. This process is involved in the propagation of coherent wave packets linking the North Atlantic and Mediterranean storm tracks in winter. To understand the link, the Rossby wave packets have been analyzed for the winter season 2004/05 by means of wave envelope, energetic, and wave‐activity diagnostics. Two specifically selected cases are presented: one with clear propagation of the wave packet to the Mediterranean region from the North Atlantic storm track, and the other with zonal propagation of the wave packets along the central latitude of the North Atlantic storm track. The dynamical effects leading to the distinct propagation characteristics of the two cases are discussed. It is shown that the two cases make clear impacts on the horizontal flux of wave activity across a domain surrounding the Mediterranean storm track.

The propagation of finite amplitude baroclinic wave packets in the two-layer model is investigated by using the multiple-scale method. It is shown that the propagation of the wave packets can be described by the so-called unstable nonlinear Schrodinger equation which possesses envelope soliton solutions. The speeds of the solitons are independent of their amplitudes.while the width of the solitons is directly proportional to their speeds but inversely proportional to their amplitudes.

Recent experiments on propagation of picosecond acoustic wave packets in condensed matter have opened up a new, exciting area of soliton physics. Single cycle strain pulses as short as several picoseconds can be generated in a thin metallic film, yielding local strain fields of the order of 10−4. The combination of phonon dispersion and anharmonicity of the atomic interaction potential may give rise to strongly nonlinear, but stable propagation of the wave packets over a distance of the order of several millimeters in a single crystalline material. We present new results on nonlinear propagation of acoustic wave packets created by nJ femtosecond optical pulses in a lead molybdate single crystal, employing the Brillouin Scattering technique as a local probe of acoustic strain. Studies of diffraction of narrow discs of acoustic strain show anomalous diffraction of the various Fourier components constituting the wave packet. Propagation of virtually one-dimensional nature is studied by exciting the metal film over a large area using an amplified femtosecond laser. We show that these data can be interpreted by means of the Korteweg-de Vries equation and strongly suggest the development of acoustic solitons.

We use a previously proposed modified saddle point method to describe the tunneling of a rectangular wave packet through a resonant quantum system. We calculate the shape of the wave packet obtained at the quantum system output analytically for different values of the level width. The result of propagation is a wave packet that is the superposition of complementary error functions. Comparing the result with the exact numerical solution obtained without using any asymptotic methods shows a rather good coincidence. We study the propagation of Gaussian and rectangular wave packets in detail for large values of the resonance level width.

Propagation of wave packets using the complex basis function method

Honeycomb structures lead to conically degenerate points on the dispersion surfaces. These spectral points, termed as Dirac points, are responsible for various topological phenomena. In this paper, we investigate the generalized honeycomb-structured materials, which have six inclusions in a hexagonal cell. We obtain the asymptotic band structures and corresponding eigenstates in the subwavelength regime using the layer potential theory. Specifically, we rigorously prove the existence of the double Dirac cones lying on the 2nd-5th bands when the six inclusions satisfy an additional symmetry. This type of inclusions will be referred to as super honeycomb-structured inclusions. Two distinct deformations breaking the additional symmetry, contraction and dilation, are further discussed. We prove that the double Dirac cone disappears, and a local spectral gap opens. The corresponding eigenstates are also obtained to show the topological differences between these two deformations. Direct numerical simulations using finite element methods agree well with our analysis.

A practical search technique for finding the complex saddle points used in wave packet and coherent state propagation is developed which works for a large class of Hamiltonian dynamical systems with many degrees of freedom. The method can be applied to problems in atomic, molecular, and optical physics and other domains. A Bose-Hubbard model is used to illustrate the application to a many-body system where discrete symmetries play an important and fascinating role. For multidimensional wave packet propagation, locating the necessary saddles involves the seemingly insurmountable difficulty of solving a boundary value problem in a high-dimensional complex space, followed by determining whether each particular saddle found actually contributes. In principle, this must be done for each propagation time considered. The method derived here identifies a real search space of minimal dimension, which leads to a complete set of contributing saddles up to intermediate times much longer than the Ehrenfest timescale for the system. The analysis also gives a powerful tool for rapidly identifying the various dynamical regimes of the system.

By using a two‐dimensional, full‐implicit‐continuous‐Eulerian (FICE) scheme, we simulated the nonlinear propagation and evolution of gravity wave packets in a compressible, nonisothermal and dissipative atmosphere. The numerical results show that when an upgoing gravity wave packet is generated in the lower mesosphere, it can propagate along its ray path until it reaches lower thermosphere. However, upon reaching the lower thermosphere, the wave packet and associated energy propagate almost horizontally, which departs obviously from the prediction of linear gravity wave theory under WKB approximation in the nondissipative case. Further discussion indicates that the influences of nonlinearity and background temperature are not strong enough to restrict completely the upward energy propagation of the wave packet and that the influence of constant molecular viscosity on the characteristics (energy propagation path and wave parameters) of gravity waves is insignificant. It is the vertical inhomogeneity of molecular viscosity that causes the restriction of upward energy propagation of the gravity wave packet. Moreover, throughout propagation, the dominant vertical wavelength of the wave packet decreases with time, as it is affected by the joint actions of nonlinearity, background temperature, and dissipation. These results indicate that the molecular viscosity, especially the vertical inhomogeneity of molecular viscosity, plays an important role in the nonlinear propagation of gravity wave packets.

The propagation of wave packets in a dispersive and anisotropic medium is formulated generally. An amplitude function is found to be a crucial auxiliary function that describes the three-dimensional propagation of a wave packet. This amplitude function, satisfying a differential equation, contains competing processes of dispersion and anisotropy in distorting the pulse. Once found, it must be further manipulated to obtain the field vector. As examples, this formulation is applied to propagation of two kinds of waves; gravity waves in a rotating atmosphere and electromagnetic waves in a magnetoplasma. Contrasting from the monochromatic case, the polychromatic features in the propagation of wave packets are pointed out both in polarization properties and amplitude dispersion.

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.

We use the Dirac continuum model to study the propagation of electronic wave packets in monolayer graphene in the presence of periodically arranged circular potential steps. The time propagation of the wave packets is calculated using the split-operator method for different sizes, heights, and separations of the barriers. We found that, despite the pronounced Klein tunneling effect in graphene, the presence of a lattice of defects significantly impacts the propagation properties of the wave packets. For example, depending on the height and size of the incident wave packet, the transmission probability can decrease by more than 30%. The alteration of the polarity of the potential barriers also contributes to the transmission probabilities of the wave packets in graphene. The results obtained her e provide valuable insights into the fundamental understanding of charge carrier dynamics in graphene-based nanodevices. • Wave-packet dynamics in graphene with periodic potential barriers are investigated. • Barrier height and arrangement show a strong influence on transmission probability. • Polarity changes of potential barriers significantly affect wave-packet propagation. • Findings provide insights into defect-induced transport in graphene nanodevices.

Excitation transfers between linear AlNC and AlCN via the à (1)Π (1 (1)A", 2 (1)A')-X (1)Σ(+) transition were studied by a wave packet propagation method as applied to a simple system for an isomerization reaction. The photoabsorption and fluorescence spectra calculated in this work are in good agreement with Einstein's A and B coefficients reported in our previous paper [I. Tokue and S. Nanbu, J. Chem. Phys. 124, 224301 (2006)]. In the 2 (1)A'-X (1)Σ(+) excitation of linear AlNC, both isomerization to linear AlCN and dissociation to Al + CN can occur; the probability of both decay channels strongly depends on the vibrational modes of the initial wave packet. The 1 (1)A"-X (1)Σ(+) excitation of linear AlNC results primarily in dissociation with isomerization being found to be a relatively minor phenomenon. For the linear AlCN excitation, vibrational levels above 1000 cm(-1) occur for both isomerization and dissociation. The isomerization of AlNC ↔ AlCN was found to occur after the à (1)Π-X (1)Σ(+) fluorescence of AlNC and AlCN, with even the initial wave packet being made with the vibrational ground level of the à (1)Π state, whereas no dissociation was recognized for any of the cases calculated in this study using lower vibrational levels as initial wave packets. The procedure for wave packet propagation employed in this study is concluded to be very effective for analyzing in detail the reaction dynamics of isomerization for triatomic molecules.

We compute the rotationally resolved differential cross sections for F(2P3/2)+D2(v=0,j) inelastic scattering as well as opacity functions for D2 rotational excitation and the reaction F+D2→D+DF. Two values of the collision energy (89.7 and 187 meV) and two initial D2 rotational states (j=0 and j=1) are probed. Four calculation techniques have been compared: the quasiclassical trajectory approach and the Wigner method on the ground state (12A′) surface, wave packet propagation (with the D2 vibrational degree of freedom treated quantum mechanically) on the 12A′ surface, and wave packet propagation on the two coupled surfaces 12A′ and 22A′. The effect of the nonadiabatic spin–orbit coupling on the nonreactive F+D2 scattering is almost negligible, whereas the reaction cross sections in the two-surface wave packet propagation treatment are considerably smaller than those in the calculations taking into account the ground state surface only.

We study propagation of high-frequency wave packets along a large-scale background wave, which evolves according to dispersionless hydrodynamic equations for two variables (fluid density and flow velocity). Influence of the wave packet on evolution of the background wave is neglected, so the large-scale evolution can be found independently of the wave packet's motion. At the same time, propagation of the packet depends in an essential way on the background wave, and it can be considered in a framework of the geometric optics approximation with the use of Hamilton equations for the carrier wave number and the mean co-ordinate of the packet. We derive equations for the carrier wave number as a function of the parameters, which describe the background wave. When they are solved, the path of the packet can be found by simple integration of the Hamilton equation. The theory is illustrated by its application to the problem of propagation of wave packets along expanding a large-scale wave, in which evolution is described by the shallow water equations. In particular, they correspond to the dispersionless limit of the defocusing nonlinear Schrödinger equation, and then the expanding wave can be considered as an expanding cloud of the Bose–Einstein condensate. Reflection of wave packets from upstream flows and their propagation along stationary flows are also discussed. The analytical solutions found for these particular cases agree very well with an exact numerical solution of the nonlinear Schrödinger equation.

It is shown that the velocity of propagation of a frequency-modulated wave packet through a strongly dispersive absorbing medium can be significantly different from (either higher or lower than) that of a non-frequency-modulated wave packet. This difference is attributed to the absorption dispersion of the medium. The easiest way to take the absorption dispersion into account is to use the formalism of the complex group velocity of a wave packet. This paper considers the propagation of a linear frequency-modulated wave packet, whose carrier frequency is close to the frequency of a spectral absorption line of the medium.