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The free evolution of a non-relativistic charged particle is manipulated using time-dependent magnetic fields. It is shown that the application of a programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to 'go back in time' to recover its past shape. The possibility of more general operations upon the Schrodinger wave packet is discussed.
A test particle approach is used to compare gyroresonant pitch angle scattering of energetic electrons by coherent versus incoherent whistler mode waves, for the case in which the coherent wave amplitude is below the nonlinear phase trapping threshold. Wave packets of 400 ms duration propagating along the magnetic field at L = 4 within the plasmasphere are considered, and the wave-induced pitch angle scattering along the propagation path from one hemisphere to the other and the resulting precipitation flux are computed. An incoherent wave spectrum is simulated by random modulation of the wave frequency at intervals of 1 ms, thereby generating signals with nearly constant power spectral density over a bandwidth of 2 kHz centered at 5.5 kHz. The associated pitch angle scattering is compared with that of a monochromatic 5.5-kHz signal of 400 ms duration. Results of the test particle analysis are compared with those expected on the basis of a classical diffusion treatment, and an expression is derived for an effective “diffusion” coefficient for pitch angle scattering by coherent waves. The trajectory followed by a particle when interacting with incoherent waves essentially represents a random walk in velocity space, while for coherent waves the pitch angle of the particle varies in a well-defined manner. In spite of the fact that individual particle scatterings are typically larger for coherent waves, the peak precipitation fluxes induced by incoherent waves are found to be approximately the same as those for coherent waves having the same total power. This results from the fact that incoherent waves interact with particles over a wider range of energies. As a consequence, the energy spectrum and the temporal extent of transient precipitation pulses due to incoherent wave packets are broader than those for equivalent coherent ones.
Freestream turbulence of weak but adjustable intensity incident upon a flat plate test model induced Tollmien-Schichting (TS) waves and wave packets. These were studied using a newly-developed sensor by which the packets could be followed from a station nearly as far forward as the minimum critical Reynolds number to the onset of transition. Conclusions reached from these studies were: (1) weak freestream turbulence induced TS wave packets in a Blasius boundary-layer, (2) packets gained strength during propagation through expansion of lateral and longitudinal scales, and through an increase in peak amplitude, (3) the average wave strength at stations of observation was not related to the freestream velocity fluctuation in a linear manner, and (4) packets typically evolved into turbulent spots.
Highly energetic electrons in the Earths Van Allen radiation belts can cause serious damage to spacecraft electronic systems and affect the atmospheric composition if they precipitate into the upper atmosphere. Whistler mode chorus waves have attracted significant attention in recent decades for their crucial role in the acceleration and loss of energetic electrons that ultimately change the dynamics of the radiation belts. The distribution of these waves in the inner magnetosphere is commonly presented as a function of geomagnetic activity. However, geomagnetic indices are nonspecific parameters that are compiled from imperfectly covered ground based measurements. The present study uses wave data from the two Van Allen Probes to present the distribution of lower band chorus waves not only as functions of single geomagnetic index and solar wind parameters but also as functions of combined parameters. Also the current study takes advantage of the unique equatorial orbit of the Van Allen Probes to estimate the average scale size of chorus wave packets, during close separations between the two spacecraft, as a function of radial distance, magnetic latitude, and geomagnetic activity, respectively. Results show that the average scale size of chorus wave packets is approximately 13002300 km. The results also show that the inclusion of combined parameters can provide better representation of the chorus wave distributions in the inner magnetosphere and therefore can further improve our knowledge of the acceleration and loss of radiation belt electrons.
We study collective processes for an electron beam propagating through a background plasma using simulations and analytical theory. A new regime where the instability of a Langmuir wave packet can grow locally much faster than ion frequency is clearly identified. The key feature of this new regime is an electron modulational instability that rapidly creates a local Langmuir wave packet, which in its turn produces local charge separation and strong ion density perturbations because of the action of the ponderomotive force, such that the beam-plasma wave interaction stops being resonant. Three evolution stages of the process and observed periodic burst features are discussed. In conclusion, different physical regimes in the plasma and beam parameter space are demonstrated for the first time.
This paper investigates the nonlinear instability of internal gravity waves and the effects of their nonlinear interaction on momentum flux, using simple theoretical and numerical models. From the result of an analysis of parametric instability of a two-dimensional internal gravity wave as discussed by Yeh and Liu (1981) and Klostermeyer (1982), a group trajectory length scale for a gravity wave packet was determined, expressed in terms of the dominant vertical wavelenght and the degree of convective saturation. It is shown that this analysis justifies the Eikonal saturation method for relatively transient packets, that are well below the saturation amplitude, propagating in a slowly varying mean flow. Conversely, linear theory fails for persistent disturbances and trasient wave packets near convective saturation.
Metamaterials are artificial structures that can manipulate and control sound waves in ways not possible with conventional materials. While much effort has been undertaken to widen the bandgaps produced by these materials through design of heterogeneities within unit cells, comparatively little work has considered the effect of engineering heterogeneities at the structural scale by combining different types of unit cells. In this paper, we use the relaxed micromorphic model to study wave propagation in heterogeneous metastructures composed of different unit cells. We first establish the efficacy of the relaxed micromorphic model for capturing the salient characteristics of dispersive wave propagation through comparisons with direct numerical simulations for two classes of metamaterial unit cells: namely phononic crystals and locally resonant metamaterials. We then use this model to demonstrate how spatially arranging multiple unit cells into metastructures can lead to tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping. In the case of the broadband wave attenuation application, we show that by building layered metastructures from different metamaterial unit cells, we can slow down or stop wave packets in an enlarged frequency range, while letting other frequencies through. In the case of the rainbow-trapping application, we show that spatial arrangements of different unit cells can be designed to progressively slow down and eventually stop waves with different frequencies at different spatial locations. Finally, in the case of the pulse-shaping application, our results show that heterogeneous metastructures can be designed to tailor the spatial profile of a propagating wave packet. Collectively, these results show the versatility of the relaxed micromorphic model for effectively and accurately simulating wave propagation in heterogeneous metastructures, and how this model can be used to design heterogeneous metastructures with tailored wave propagation functionalities.
A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong-turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam-excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V/m. The existence of waves with energy densities above the strong-turbulence wave-collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion-sound waves are also consistent with the observations. It is shown that strong-turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.
We present UV pump, vacuum ultraviolet probe time-resolved photoelectron spectroscopy measurements of the excited state dynamics of cis,cis-1,3-cyclooctadiene. A 4.75 eV deep UV pump pulse launches a vibrational wave packet on the first electronically excited state, and the ensuing dynamics are probed via ionization using a 7.92 eV probe pulse. The experimental results indicate that the wave packet undergoes rapid internal conversion to the ground state in under 100 fs. Comparing the measurements with electronic structure and trajectory surface hopping calculations, we are able to interpret the features in the measured photoelectron spectra in terms of ionization to several states of the molecular cation.
Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be bounded-error quantum polynomial time (BQP) complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wave packets in one-dimensional scalar field theory is simulated using 120 qubits of IBM’s Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wave packet initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical matrix product state simulations. Finally, the developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.
We describe the interaction of parallel-propagating Alfvén waves with ion-acoustic waves and other Alfvén waves, in magnetized, high- β collisionless plasmas. This is accomplished through a combination of analytical theory and numerical fluid simulations of the Chew–Goldberger–Low (CGL) magnetohydrodynamic (MHD) equations closed by Landau-fluid heat fluxes. An asymptotic ordering is employed to simplify the CGL-MHD equations and derive solutions for the deformation of an Alfvén wave that results from its interaction with the pressure anisotropy generated either by an ion-acoustic wave or another, larger-amplitude Alfvén wave. The difference in time scales of acoustic and Alfvénic fluctuations at high- β means that interactions that are local in wavenumber space yield little modification to either mode within the time it takes the acoustic wave to Landau damp away. Instead, order-unity changes in the amplitude of Alfvénic fluctuations can result after interacting with frequency-matched acoustic waves. Additionally, we show that the propagation speed of an Alfvén-wave packet in an otherwise homogeneous background is a function of its self-generated pressure anisotropy. This allows for the eventual interaction of separate co-propagating Alfvén-wave packets of differing amplitudes. The results of the CGL-MHD simulations agree well with these predictions, suggesting that theoretical models relying on the interaction of these modes should be reconsidered in certain astrophysical environments. Applications of these results to weak Alfvénic turbulence and to the interaction between the compressive and Alfvénic cascades in strong, collisionless turbulence are also discussed.
We report a study of the quantum beats in two-color photoionization of argon. An attosecond extreme ultraviolet pulse train prepares an electronic wave packet of definite odd parity, with total angular momentum J = 1, targeting the states between 14.0 and 14.5 eV from the ground state. Two-photon ionization of this wave packet with a tunable infrared probe pulse makes the constituent states interfere in both continuum channels, corresponding to the core angular momenta j c = 1/2 and 3/2, respectively. We analyze photoelectron spectrograms as a function of the time delay of the probe pulse and identify oscillations due to several pairs of states through Fourier decomposition. We observe phase differences between the corresponding beat signals in the two spin-orbit split continua. Comparison of theoretical simulations with the experimental measurements allows us to interpret the amplitudes and phases of ionization signals. Furthermore, we express the observed phase differences in terms of the off-diagonal elements of the short-range scattering matrix and the dipole matrix elements to the continuum eigenchannels.
A theory has been developed to interpret time-domain Brillouin scattering (TDBS) experiments involving coherent acoustic pulse (CAP) and light pulse beams propagating at an angle to each other. It predicts the influence of the directivity pattern of their acousto-optic interaction on TDBS signals when heterodyne detection of acoustically scattered light is in backward direction to incident light. The theory reveals relationships between the carrier frequency, amplitude and duration of acoustically induced ”wave packets” in light transient reflectivity signals, and factors such as CAP duration, widths of light and sound beams, and their interaction angle. It describes the transient dynamics of these wave packets when the light and CAP encounter material interfaces, and how the light scattering by the incident CAP transforms into scattering by the reflected and transmitted CAPs. The theory suggests that single-point TDBS experiments can determine not only depth positions of buried interfaces but also their local inclinations/orientations.
Conical intersections between electronic states often dictate the chemistry of photoexcited molecules. Recently developed sources of ultrashort extreme ultraviolet (XUV) pulses tuned to element-specific transitions in molecules allow for the unambiguous detection of electronic state-switching at a conical intersection. Here, the fragmentation of photoexcited iso-propyl iodide and tert-butyl iodide molecules (i-C 3 H 7 I and t-C 4 H 9 I) through a conical intersection between 3 Q 0 / 1 Q 1 spin-orbit states is revealed by ultrafast XUV transient absorption measuring iodine 4d core-to-valence transitions. The electronic state-sensitivity of the technique allows for a complete mapping of molecular dissociation from photoexcitation to photoproducts. In both molecules, the sub-100 fs transfer of a photoexcited wave packet from the 3 Q 0 state into the 1 Q 1 state at the conical intersection is captured. The results show how differences in the electronic state-switching of the wave packet in i-C 3 H 7 I and t-C 4 H 9 I directly lead to differences in the photoproduct branching ratio of the two systems.
Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this Letter, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. Here, the framework and protocol are applicable if the potential is harmonic over the extent of the ion wave packets at all times. As illustrations, we discuss two specific operations: changing the strength of the confining potential for a single ion and separating same-species ions with their mutual Coulomb force. Both of these operations are, ideally, free of residual motional excitation.
The quantum acoustic framework has recently emerged as a nonperturbative, coherent approach to electron–lattice interactions, uncovering rich physics often obscured by perturbative methods with incoherent scattering events. Here, we model the strongly coupled dynamics of electrons and acoustic lattice vibrations within this framework, representing lattice vibrations as coherent states and electrons as quantum wave packets, in a manner distinctively different from tight-binding or discrete hopping-based approaches. We derive and numerically implement electron backaction on the lattice, providing both visual and quantitative insights into electron wave packet evolution and the formation of acoustic polarons. We investigate polaron binding energies across varying material parameters and compute key observables—including mean square displacement, kinetic energy, potential energy, and vibrational energy—over time. Our findings reveal the conditions that favor polaron formation, which is enhanced by low temperatures, high deformation potential constants, slow sound velocities, and high effective masses. Additionally, we explore the impact of external electric and magnetic fields, showing that while polaron formation remains robust under moderate fields, it is weakly suppressed at higher field strengths. These results deepen our understanding of polaron dynamics and pave the way for future studies into nontrivial transport behavior in quantum materials.
The role of geostrophic adjustment in the middle atmosphere for given wave packet forcing by a three-dimensional hydrostatic model is examined. It is shown that the induced fields consist of two different kinds of modes. One, produced by forcing vorticity only, is steady quasi-geostrophic flow; this is restricted to the forcing region. The other, produced by both forcing vorticity and forcing divergence, is oscillatory, and is in the form of gravity waves propagating out of the forcing region plus inertial oscillations in the forcing region. The scales and amplitudes of the induced gravity waves are determined by the forcing. For a typical example, a 200 km x 200 km gravity wave packet of momentum flux 0.5 N/sq m absorbed in a layer of 5 km thickness centered near 18 km altitude, the gravity waves spread to a larger region about 1000 km x 1000 km at a level 7 km above the forcing region. At that level, the horizontal and vertical wavelengths of the induced waves are about 300 km and 7 km respectively, and the momentum flux is substantially reduced to 0.0004 N/sq m. The results suggest that geostrophic adjustment processes may play an important role in specifying the gravity wave spectrum in the middle atmosphere.
The nonlinear properties of the amplitude-modulated circularly polarized Alfven wave are studied for beta less than one. The temporal behavior of the wave packet of the electromagnetic hybrid simulation is compared with a numerical solution of the derivative nonlinear Schroedinger (DNLS) equation. It is shown that the left-hand-polarized mode evolves into a shocklike structure due to the modulational instability. However, both cyclotron damping and a snowplow effect near the steepened wave packet suppress its further steepening, contrary to the predictions of the DNLS equation. For the right-hand mode, formation of the shock does not take place, and the initial time development is well described by the DNLS equation. The daughter Alfven wave and ion acoustic waves are excited due to the decay instability at a later time. Heating or acceleration of the particles takes place for both left- and right-hand waves. Energy transfer from the wave to the particles occurs effectively when substantial modulation in the wave amplitude is present.