Wave Packets in a Magnetic Field

A Gaussian wave packet confined to move on a plane perpendicular to a magnetic field remains a Gaussian wave packet in its time evolution. The average position and momentum follow the Ehrenfest equations which are identical to the classical Hamilton equations. A set of nonlinear equations decoupled from the Ehrenfest equation is derived for the parameters describing the time evolution of the density distribution and phases of a wave packet. Explicit solutions are then obtained when the "internal" angular momentum of the wave packet vanishes. In this case it is shown that the motion of the wave packet is a superposition of a translational motion, a rotation and a vibration.     

Dynamics of a two-wave packet in a nonlinear optical fiber at detuning from phase matching

The effect of detuning from phase matching on the dynamics of a wave packet consisting of two unidirectional strongly interacting modes in a fiber with Kerr nonlinearity is considered. The effective parameters of dispersion and nonlinearity are analyzed for a wave packet that can be represented by a single partial pulse.     

Zitterbewegung in the honeycomb photonic lattice

The propagation of a wave packet in a honeycomb photonic lattice has been studied using the time-dependent wave packet dynamics. It is found that the wave packet, superposed from the positive and negative energy modes at the vicinity of the two inequivalent Dirac points, can transform into a double-ring structure, which is caused by the interference between the two positive and negative energy modes around the Dirac points and is closely related to the Zitterbewegung (ZB). Also, a possible way to detect the ZB effect is proposed in the honeycomb photonic lattice.     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Absence of wave packet diffusion in disordered nonlinear systems

We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schr?dinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.     

Nonlinear evolution of a three-dimensional transverse wave packet in a hot plasma including the effect of its interaction with an ion-acoustic wave

By a perturbation method two coupled nonlinear partial differential equations are obtained for the nonlinear evolution of a three dimensional transverse wave packet in a hot plasma including the effect of its interaction with a long wavelength ion-acoustic wave. From these two equations a nonlinear dispersion relation is obtained, from which the instability condition of a uniform transverse wave train including the effect of its interaction, both at resonance and at nonresonance with a long wavelength ion-acoustic wave, are deduced. Resonance occurs when the component of group velocity of the longitudinal wave along the direction of propagation of the ion-acoustic wave is equal to the phase velocity of the wave. Assuming the usual type of dependence of amplitude on space and time the coupled equations are transformed into two other coupled equations, which reduced to a single nonliear Schrödingsr equation when three dimensionality is disregarded. It is found that these three transformed equations cannot give instability condition at resonance.On leave fromThe Department of Mathematics, University of Kalyani, West Bengal, India.     

Multiphoton stimulated bremsstrahlung for broad (in the momentum representation) electron wave packets in an ultrashort laser pulse field

We consider features of absorption and emission of external laser field quanta by a broad (in the momentum representation) electron wave packet during its scattering from a potential center. Various scattering modes for the electron wave packet in a high-intensity laser field are analyzed using perturbation theory of potential energy. It is found that the absorption of laser field energy by an electron is substantially more effective as compared to the case of a plane wave. The important role of a number of interference effects associated with the large width of the initial electron momentum distribution is demonstrated.     

On the existence of higher waves in a layer of superfluid helium

The two implicit equations that contain the dispersion laws of waves propagating in a He II layer of variable thickness are formally investigated for solutions that go beyond those associated with the layer modifications of first and second sound: A series of symmetric and antisymmetric layer modes are found to exist by calculating the distribution of roots of the dispersion equations in the complex wave number plane as a function of layer thickness and angular frequency. All these modes turn out to be strongly attenuated and can be regarded as layer modifications of the viscous wave. Phase velocities, attenuation coefficients, and velocity profiles of some of them are calculated numerically.     

Secondary instabilities of interfacial waves due to coupling with a long wave mode in a two-layer Couette flow

We report experiments on the stability of interfacial waves in a two-layer Couette flow. As the shear rate is increased, the periodic wave train arising from the primary instability undergoes a secondary instability which results in wave coalescence or nucleation, after a long transient. This secondary instability crucially involves the coupling with a long wave mode, which corresponds to variations of the mean interface level. These observations are favourably compared to stability results on travelling wave solutions for a set of two coupled equations, one for the envelope of a weakly unstable wave packet, and the other for the marginal long wave mode with zero wave number. A physical mechanism for this instability is proposed, as well as an interpretation for the onset of chaos.     

Resonant interaction of an electromagnetic wave with an inhomogeneous plasma slab

Resonant interaction at oblique incidence of an electromagnetic wave on an inhomogeneous plasma slab is studied. The time evolution of this interaction is solved numerically from two-fluid equations, adiabatic equation for electron pressure and from Maxwell equations. It is shown that the electromagnetic energy of an incident wave is transformed both into the heat energy and into the energy of plasma oscillations in the direction of density gradient. The distribution of the transformed energy between the heat energy and the energy of plasma oscillations is strongly dependent on the plasma temperature. The ratio of heat energy to the energy of plasma oscillations is growing with growing temperature. The plasma oscillations are generated by magnetic induction of the penetrating wave. In a cold plasma they are generated especially in the overdense region and their frequency is equal to local plasma frequency. The electric field in the direction of plasma gradient has a form of a wave packet whose envelope reaches a maximum at resonance. The characteristic wavelength in the wave packet decreases and the amplitude of the packet increases with the time.     

Certain singular solutions to Pauli's equation

Green's time functions are constructed for a neutral Pauli particle in nonuniform magnetic fields of special modes and, in the subsequent analysis, the motion of such a particle is regarded as an evolution (in time) of a Gaussian wave packet.     

Acoustic multipath arrivals in the horizontal plane due to approaching nonlinear internal waves

Simultaneous measurements of acoustic wave transmissions and a nonlinear internal wave packet approaching an along-shelf acoustic path during the Shallow Water 2006 experiment are reported. The incoming internal wave packet acts as a moving frontal layer reflecting (or refracting) sound in the horizontal plane. Received acoustic signals are filtered into acoustic normal mode arrivals. It is shown that a horizontal multipath interference is produced. This has previously been called a horizontal Lloyd's mirror. The interference between the direct path and the refracted path depends on the mode number and frequency of the acoustic signal. A mechanism for the multipath interference is shown. Preliminary modeling results of this dynamic interaction using vertical modes and horizontal parabolic equation models are in good agreement with the observed data.     

Drift theory of the resonant interaction of charged particles with wave packets

Averaged equations of motion are obtained for charged particles resonantly interacting with high-frequency wave packets in the case of finite cyclotron radius. It is shown that the mean action of the packet on the particle is not a potential function. Cherenkov resonance of particles with the beats of two wave packets in inhomogeneous plasma is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–13, April, 1982.     

Baroclinic wave packets described by spatially varying Lorenz equations

Solutions are obtained numerically for the evolution in space and time of the amplitude of a baroclinic wave packet in a weakly viscous fluid. The behaviour observed is confirmed analytically to resemble that occuring for wave trains, described by the Lorenz attractor equations, at a modified value of the viscosity parameter.     

Nondegenerate soliton solutions in certain coupled nonlinear Schrödinger systems

In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schrödinger type equations through bilinearization procedure. In particular, we consider coupled nonlinear Schrödinger (CNLS) equations (both focusing as well as mixed type nonlinearities), coherently coupled nonlinear Schrödinger (CCNLS) equations and long-wave-short-wave resonance interaction (LSRI) system. We point out that the obtained general form of soliton solutions exhibit novel profile structures than the previously known degenerate soliton solutions corresponding to identical wave numbers in both the modes. We show that such degenerate soliton solutions can be recovered from the newly derived nondegenerate soliton solutions as limiting cases.     

Nonlinear distribution function for a plasma obeying Vlasov-Maxwell system of equations

The nonlinear distribution function of Allis, generalised to include the transverse electromagnetic waves in a plasma, is used to set up the coupled wave equations for the longitudinal and the transverse modes. These are solved, keeping terms up to the cubic order of nonlinearity, by using the method of multiple scales. The equations of wave modulation are derived, which are solved to discuss the nature of the modulational instability and solitary wave propagation. It is found that the solutions so obtained satisfy conditions which are very similar to the well known Lighthill criterion for stability, appropriately modified due to the coupling of the two modes. The role of the average constant current due to any flow of the resonant and trapped electrons in determining the stability, is also discussed.     

Stueckelberg Oscillations in a Two‐State Two‐Path Model of a Conical Intersection

The two‐state two‐path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi‐classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.     

间接馈电柱-锥级联爆磁压缩发生器数值模拟

为了研究间接馈电、两级级联柱-锥构型的爆磁压缩发生器的物理特性，发展了描述爆磁压缩物理过程的2维爆轰磁流体力学程序——MFCG（Ⅴ），并用其分析、计算了一系列模型。通过将计算结果与柱-柱构型的结果进行比较，表明了柱-锥构型更有利于功率放大:在同样的输出电流条件下，不仅爆磁压缩的时间缩短，而且输出功率也相应地增加。MFCG（Ⅴ）程序的建立以及相应的数值模拟结果有助于加深对柱-锥构型的爆磁压缩发生器物理过程的认识，并为实验设计提供参考。     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

波包的空时演化与能级免交叉

采用二维谐振子相干态为初始态,在形变原子核系统分别为规则和混沌两种情况下,对其在相空间中的时间行为进行了傅里叶分析,特别比较了混沌系统中波包宽度在整个时间段与达到饱和后两个阶段的傅里叶分析结果.指出系统的混沌运动是由于大量能级免交叉的出现在波包运动的初始阶段就破坏了波包内部的规则结构,波包各成分间的协同性被破坏,波包的运动成为混沌.此后,波包内各成分对波包运动的贡献开始相同,能级之间的免交叉对波包运动的影响也不再明显.