Form Of Wave Packets Research Articles

On the response of large-amplitude internal waves to upstream disturbances

AbstractLarge-amplitude internal solitary waves generate shear flows that intensify from the wings of the waves to their maxima. Upstream perturbations of the hydrostatic equilibrium in the form of wave packets along the path of wave propagation are expected to trigger shear instability and ultimately generate Kelvin–Helmholtz roll-ups. In contrast, as shown here with accurate simulations of incompressible stratified Euler equations, large internal waves can act as suppressors of perturbations. The precise understanding of the mechanisms leading to different outcomes, including whether instability is excited, is the focus of this work. Under the action of shear flows, small-amplitude wave packets undergo stretching and filamentation, which lead to significant absorption of perturbation energy into the background shear. It is found that this typical behaviour is present in the self-induced shear by internal waves, regardless of whether the shear is stable or unstable, and can leave a quieter state in the wave’s wake for a wide range of perturbation parameters. In the unstable case, even once perturbations are selected to excite the instability, our results show that this absorption can act to reduce growth in the strong-shear region, effectively making roll-up development observable only downstream of the wave crest. Our approach is both analytical and numerical; a model valid for relatively thin pycnoclines and suitable for local spectral analysis is devised and used. Energy diagnostics on the simulations are implemented to validate the numerics and illustrate the energy exchanges between background wave flow and its shear. A link between the absorption mechanism and the clustering of local eigenvalues along the wave is proposed. This promotes an energetic coupling among neutral modes stronger than what may be expected to occur in slowly varying flows, and gives rise to multi-modal transient dynamics of the kind often referred to as non-normality effects. For those cases in which the wave-induced shear meets the conditions for local instability, it is found that the growth of disturbances is selective with respect to the sign of the mode excited upstream. Elements of this phenomenon are interpreted by asymptotic analysis for spatial growth in time-independent slowly varying media.

Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times

We develop a wavepacket approach to the diffraction of charged particles by a thin material target and we use the de Broglie–Bohm quantum trajectories to study various phenomena in this context. We construct a particle wave function model given as the sum of two terms ψ = ψ ingoing + ψ outgoing , each having a wavepacket form with longitudinal and transverse quantum coherence lengths both finite. We find the form of the separator, i.e. the limit between the domains of prevalence of the ingoing and outgoing quantum flow. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of quantum vortices (nodal point — X point complexes). The X point gives rise to stable and unstable manifolds, whose directions determine the scattering of the de Broglie–Bohm trajectories. We show how the deformation of the separator near Bragg angles explains the emergence of a diffraction pattern by the de Broglie–Bohm trajectories. We calculate the arrival time distributions for particles scattered at different angles. A main prediction is that the arrival time distributions have a dispersion proportional to v 0 − 1 × , the largest of the longitudinal and transverse coherence lengths, where v 0 is the mean velocity of incident particles. We also calculate time-of-flight differences Δ T for particles scattered in different angles. The predictions of the de Broglie–Bohm theory for Δ T turn out to be different from estimates of the same quantity using other theories on time observables like the sum-over-histories or the Kijowski approach. We propose an experimental setup aiming to test such predictions. Finally, we explore the semiclassical limit of short wavelength and short quantum coherence lengths, and demonstrate how, in this case, results with the de Broglie–Bohm trajectories are similar to the classical results of Rutherford scattering.

Continuous spectra of the Batchelor vortex

The spectra of the Batchelor vortex are obtained by discretizing its linearized evolution operator using a modified Chebyshev polynomial approximation at a Reynolds number of 1000 and zero azimuthal wavenumber. Three types of eigenmodes are identified from the spectra: discrete modes, potential modes and free-stream modes. The discrete modes have been extensively documented but the last two modes have received little attention. A convergence study of the spectra and pseudospectra supports the classification that discrete modes correspond to discrete spectra while the other two modes correspond to continuous spectra. Free-stream modes have finite amplitude in the far field whilst potential modes decay to zero in the far field. The free-stream modes are therefore a limiting form of the potential modes when the radial decay rate of velocity components reduces to zero. The radial form of the free-stream modes with axial and radial wavenumbers is investigated and the penetration of the free-stream mode into the vortex core highlights the possibility of interaction between the potential region and the vortex core. A wavepacket pseudomode study confirms the existence of continuous spectra and predicts the locations and radial wavenumbers of the eigenmodes. The pseudomodes corresponding to the potential modes are observed to be in the form of one or two wavepackets while the free-stream modes are not observed to be in the form of wavepackets.

Dynamics of unitarization by classicalization

We study dynamics of the classicalization phenomenon suggested in G. Dvali et al. [1], according to which a class of non-renormalizable theories self-unitarizes at very high-energies via creation of classical configurations (classicalons). We study this phenomenon in an explicit model of derivatively-self-coupled scalar that serves as a prototype for a Nambu–Goldstone–Stückelberg field. We prepare the initial state in form of a collapsing wave-packet of a small occupation number but of very high energy, and observe that the classical configuration indeed develops. Our results confirm the previous estimates, showing that because of self-sourcing the wave-packet forms a classicalon configuration with radius that increases with center of mass energy. Thus, classicalization takes place before the waves get any chance of probing short-distances. The self-sourcing by energy is the crucial point, which makes classicalization phenomenon different from the ordinary dispersion of the wave-packets in other interacting theories. Thanks to this, unlike solitons or other non-perturbative objects, the production of classicalons is not only unsuppressed, but in fact dominates the high-energy scattering. In order to make the difference between classicalizing and non-classicalizing theories clear, we use a language in which the scattering cross section in a generic theory can be universally understood as a geometric cross section set by a classical radius down to which waves can propagate freely, before being scattered. We then show, that in non-classicalizing examples this radius shrinks with increasing energy and becomes microscopic, whereas in classicalizing theories expands and becomes macroscopic. We study analogous scattering in a Galileon system and discover that classicalization also takes place there, although somewhat differently. We thus observe, that classicalization is source-sensitive and that Goldstones pass the first test.

Alfven soliton and multisoliton dynamics perturbed by nonlinear Landau damping

The evolution of weakly dispersive nonlinear Alfven waves propagating either parallel or oblique to the ambient magnetic field is investigated through the derivative nonlinear Schrödinger equation (DNLS) perturbed by nonlinear Landau damping. The dynamics is analyzed with the aid of a numeric algorithm based on the inverse scattering transform (IST) and an adiabatic model that takes advantages of the perturbed DNLS invariants. Both techniques are applied to five types of DNLS soliton and multisoliton solutions: (i) the parallel Alfven soliton, (ii) the bright and dark one-parameter oblique, (iii) the breather two-parameter oblique, (iv) two parallel Alfven solitons, and (v) the combination of a dark and a bright oblique solitons. For the parallel solitons, the adiabatic model describes correctly the dynamics and it also recovers the well-known result given by the perturbed IST. Due to the radiation emission and the formation of dark solitons, the behavior of oblique solitons is more complicated and multisoliton solutions are required in the adiabatic model. The analysis shows that parallel solitons develop into the normal regime, whereas the oblique waves leads to the formation of dark solitons and breathers with a wavepacket form.

On Coherence Lengths of Wave Packets

The coherence lengths of one-particle states described using quantum wave functions are studied. We show that one particle states in various situations are not described using simple plane waves but using wave packets that are superpositions of plane waves. A wave packet is an approximate eigenstate of the free Hamiltonian and has a finite spatial size that we call the coherence length. The coherence lengths in the coordinate space and momentum space are studied in this paper. We investigate several mechanisms of forming wave packets, stabilities of wave packets, and transformations of wave packets.

Revivals, classical periodicity, and zitterbewegung of electron currents in monolayer graphene

Revivals of electric current in graphene in the presence of an external magnetic field are described. It is shown that when the electrons are prepared in the form of wave packets assuming a Gaussian population of only positive (or negative) energy Landau levels, the presence of the magnetic field induce revivals of the electron currents, besides the classical cyclotron motion. When the population comprises both positive and negative energy Landau levels, revivals of the electric current manifest simultaneously with zitterbewegung and the classical cyclotron motion. We relate the temporal scales of these three effects and discuss to what extent these results hold for real graphene samples.

Interatomic coulombic decay: a short review

The transition process of the interatomic Coulombic decay (ICD), is an electronic radiationless transition process, driving molecular complexes or clusters to a doubly ionized final state. This process differs from the Auger effect, because it takes place from a neutral monomer after the absorption of a released amount energy of the neighboring monomer in the weakly bound molecule. This process has been theoretically studied and the most recent experimental evidence was observed with neon dimer. This work presents a description of the process and a detailed revision of the derivation for the distribution kinetic energy equation to the emitted electrons by ICD decay, with a small variation in the wave packet form of the transition for the final states , with non-Hermitian time-dependent theory.

Long-wave transverse instability of interfacial gravity–capillary solitary waves in a two-layer potential flow in deep water

Interfacial gravity–capillary plane solitary waves, driven by the gravitational force in the presence of interfacial tension in a two-layer deep-water potential flow, bifurcate in the form of wavepackets with a non-zero carrier wavenumber at which the phase speed is minimized. A stability property for the interfacial gravity–capillary plane solitary waves is presented within the framework of the full Euler equations: according to a linear stability analysis based on the perturbation method, such waves are unstable under weak and long-wave disturbances in the transverse direction to the dominant wave propagation. An instability criterion is verified that the total mechanical energy of the solitary waves is a decreasing function of the solitary wavespeed, owing to the fact that the speed of the bifurcating solitary wavepackets is less than the minimum of the phase speed. This result is consistent with an earlier study on the transverse instability of the longitudinally stable interfacial gravity–capillary solitary waves from the Benjamin model equation for weakly nonlinear long interfacial elevations (Kim and Akylas, J Fluid Mech 557:237–256, 2006). The analysis is also applicable to other interfacial gravity–capillary solitary waves that may bifurcate below the minimum of the phase speed, regardless of any restrictions on fluid depths in two-layer potential flows.

Zitterbewegung of electrons in graphene in a magnetic field

Electric current and spatial displacement due to trembling motion [Zitterbewegung (ZB)] of electrons in graphene in the presence of an external magnetic field are described. Contributions of both inequivalent $K$ points in the Brillouin zone of graphene are considered. It is shown that, when the electrons are prepared in the form of wave packets, the presence of a quantizing magnetic field $B$ has very important effects on ZB. (1) For $B\ensuremath{\ne}0$ the ZB oscillations are permanent while for $B=0$ they are transient. (2) For $B\ensuremath{\ne}0$ many ZB frequencies appear while for $B=0$ only one frequency is at work. (3) For $B\ensuremath{\ne}0$ both interband and intraband (cyclotron) frequencies contribute to ZB while for $B=0$ there are no intraband frequencies. (4) Magnetic field intensity changes not only the ZB frequencies but the entire character of ZB spectrum. An emission of electromagnetic dipole radiation by the trembling electrons is proposed and described. It is argued that graphene in a magnetic field is a promising system for an experimental observation of Zitterbewegung.

Dynamical study on charge injection and transport in a metal/polythiophene/metal structure

The dynamical process of charge injection from metal electrode to a nondegenerate polymer in a metal/polythiophene (PT)/metal structure has been investigated by using a nonadiabatic dynamic approach. It is found that the injected charges form wave packets due to the strong electron-lattice interaction in PT. We demonstrate that the dynamical formation of the wave packet sensitively depends on the strength of applied voltage, the electric field, and the contact between PT and electrode. At a strength of the electric field more than 3.0 × 104 V/cm, the carriers can be ejected from the PT into the right electrode. At an electric field more than 3.0 × 105 V/cm, the wave packet cannot form while it moves rapidly to the right PT/metal interface. It is shown that the ejected quantity of charge is noninteger.

Amplifier and resonator dynamics of a low-Reynolds-number recirculation bubble in a global framework

The stability behaviour of a low-Reynolds-number recirculation flow developing in a curved channel is investigated using a global formulation of hydrodynamic stability theory. Both the resonator and amplifier dynamics are investigated. The resonator dynamics, which results from the ability of the flow to self-sustain perturbations, is studied through a modal stability analysis. In agreement with the literature, the flow becomes globally unstable via a three-dimensional stationary mode. The amplifier dynamics, which is characterized by the ability of the flow to exhibit large transient amplifications of initial perturbations, is studied by looking for the two- and three-dimensional initial perturbations that maximize the energy gain over a given time horizon. The optimal initial two-dimensional perturbations have the form of wave packets localized in the upstream part of the recirculation bubble. It is shown that they are first amplified while travelling downstream along the shear layer of the recirculation bubble and then decay when leaving the recirculation bubble. Maximal energy gain is thus achieved for a time horizon approximately corresponding to the propagation of the wave packet along the whole recirculation bubble. The resonator and amplifier dynamics are associated with different types of structures in the flow: three-dimensional steady structures for the resonator dynamics and nearly two-dimensional unsteady structures for the amplifier dynamics. A comparison of the strength of the two dynamics is proposed. The transient energetic growth of the two-dimensional unsteady perturbations is large at moderate time, compared to the very weak exponential growth of the three-dimensional stationary mode. This suggests that, as soon as there is noise in the system, the amplifier dynamics dominates the resonator dynamics, thus explaining the appearance of unsteadiness rather than the emergence of stationary structures in similar experimental flows.

Dynamical study on charge injection and transport in a metal/poly(p-phenylene vinylene)/metal structure

On the basis of the tight-binding Su-Schrieffer-Heeger model， the dynamical process of charge injection from metal electrode to a polymer in a metal/poly(p-phenylene vinylene) (PPV)/metal structure has been investigated by using a nonadiabatic dynamic approach. It is found that the injected charges form wave packets due to the strong electron-lattice interaction in PPV. The formation of the wave packet sensitively depends on the applied voltage， the electric field， and the contact between PPV and the metal electrode. In the absence of external fields， the charge can be injected into PPV chain and form wave packet under the critical bias voltage. With the increase of the electric field， the charge carriers can be ejected from PPV to the right metal electrode. But when the electric field becomes high enough， the wave packet can not be formed because it moves too fast in PPV. It is also shown that the number of ejected charges is not an integral multiple of the elementary charge e.

On the non-existence of the micro-causal sector of Lorentz non-invariant quantum field theory on a continuum

We study a model for a Lorentz non-invariant quantum field theory. In this model Lorentz violation is due to a non-linear dispersion relation admitting signals in form of wave packets propagating with super-luminal (faster than the low-energy speed of light) group velocities. We characterize the causal sector of the theory by a cutoff condition protecting the theory against such signals and study the question as to whether the causal sector exhibits micro-causality (locality in all frames), in which case we call the causal sector the micro-causal sector. It is argued that in the causal sector the canonical commutation relation are changed in such a way that the imposition of locality postulate becomes incompatible with the continuity of space. The conclusion therefore is that there is no micro-causal sector of the theory on the continuum space underlying the model and in this respect it suggests the sensitivity of an effective Lorentz non-invariant quantum field theory to a short-distance cutoff.

Unruh’s detector in the presence of Lorentz symmetry breaking

We investigate the quantum field theory of a Lorentz non-invariant model with a massive nonlinear dispersion relation in Minkowski space. The model involves some non-causal signals in the form of wave packets propagating with super-luminal group velocities. To avoid the problems with causality we characterize the causal sector of the theory by a cutoff condition excluding all super-luminal group velocities. It is argued that in the causal theory satisfying the energy positivity condition an Unruh’s detector moving with a constant velocity with respect to the preferred frame does not detect any particle. But in a causal theory violating energy positivity, detection of a field quanta occurs. We comment on the origin of this particle creation.

Constructing an analytical solution for lamb waves using the cosserat continuum approach

The problem of propagation of a Lamb elastic wave in a thin plate is considered using the Cosserat continuum model. The deformed state is characterized by independent displacement and rotation vectors. Solutions of the equations of motion are sought in the form of wave packets specified by a Fourier spectrum of an arbitrary shape for three components of the displacement vector and three components of the rotation vector which depend on time, depth, and the longitudinal coordinate. The initial system of equations is split into two systems, one of which describes a Lamb wave and the second corresponds to a transverse wave whose amplitude depends on depth. Analytical solutions in displacements are obtained for the waves of both types. Unlike the solution for Lamb waves, the solution obtained for the transverse wave has no analogs in classical elasticity theory. The solution for the transverse wave is compared with the solution for the Lamb wave.

Dynamics of charge injection into an open conjugated polymer: A nonadiabatic approach

The dynamic process of charge injection is investigated for an open conjugated polymer chain in contact with a metal electrode in the framework of a nonadiabatic approach. It is found that the injected charges form wave packets due to the strong electron-lattice interactions in the conjugated polymer. A wave packet may contain any quantity of charges up to two electronic units, which depends upon the injection condition. As the system is spin degenerate within the present model, a wave packet has no spin. Discrete energy levels will appear in the gap accompanying the wave packet, which results in potential asymmetry of the charge injection and ejection between the metal electrode and the polymer. The asymmetry can be used to explain the electrical hysteresis in organic devices. It is found that there exists an upper critical field or forming field, beyond which the injected charges could not form a wave packet. Under a strong driving electric field, it is also found that a wave packet will dissociate into an extended state. The dependence of the dissociating field on the charge quantity a wave packet contains is studied.

Propagation of surface elastic waves in the Cosserat medium

The problem of surface elastic wave propagation in the Cosserat medium (half-space) is considered. The strained state is characterized by two independent vectors: displacement and rotation. Solutions to the equations of motion are sought in the form of wave packets specified by an arbitrary Fourier spectrum. It is shown that, if the solution is sought in the form of a three-component displacement vector and a three-component rotation vector dependent on time, depth, and longitudinal coordinate, the initial system splits into two systems, one of which describes the Rayleigh wave and the other corresponds to a transverse wave decaying with depth. For both waves, analytical solutions in terms of displacements are obtained. It should be particularly noted that, unlike the Rayleigh wave, the solution for the transverse surface wave has no analogues in the classical elasticity theory. The transverse wave solution is numerically compared with the Rayleigh wave solution.

Collisions Transfer Coherence

AbstractUltrafast photoexcitation of molecules prepares coherent superpositions of vibrational states, forming wave packets. We show direct experimental evidence that impulsive collisions of photo‐fragments with large energy loss generate new coherent superpositions of vibrational states, causing coherence among previously unoccupied states. We demonstrate the effect in the model system of I2 molecules in Kr solids. This coherence transfer—even in the presence of very strong dissipation—may be used for control strategies in condensed‐phase photoreactions.

Ultrafast Lattice Relaxation Phenomena Studied by Time-Resolved Luminescence Spectroscopy

Recent developments in the ultrafast luminescence spectroscopy are reviewed. Principles of time-resolved luminescence measurements i.e., the optical Kerr shutter method and the up-conversion technique are described. The formation and relaxation processes of self-trapped excitons in quasi-one-dimensional halogenbridged platinum complexes (Pt-Cl, Pt-Br, Pt-I) are studied by luminescence up-conversion technique. The lifetime of the self-trapped excitons shows a systematic decrease as the mass of the halogen ion increases, showing the increased probability of non-radiative decay processes. The real-time capturing of the nuclear wave-packet form is successfully demonstrated in Pt-Br and good agreements with calculation are obtained. The luminescence in the picosecond region has been observed in the halogen-bridged nickel complex, and a coexistence of localized excitons with small and large lattice relaxations is suggested.