Oscillating Wave Packet Research Articles

Variable dust charge generates multi solitons, breather soliton structures in Saturn’s ring

In this study, we have investigated nonlinear wave structures that are localized along with the exact stationary wave solutions with oscillating, i.e. the breather structures in an unmagnetized dusty plasma with variable dust charge concentration with two temperatures of ions. We have derived GE from the normalized governing equations employing the reductive perturbative technique (RPT). The GE is the extended Korteweg–de Vries (KdV) equation that includes the united effect of quadratic and cubic nonlinearities. Employing the Hirota bilinear method (HBM), multi-soliton solutions and the breather soliton solutions have been obtained. Breathers (oscillating wave packets) play a significant role in hydrodynamics and optics, and their interaction can change the dynamics of the wave fields. It is also important to propagate finite-amplitude waves in the astrophysical atmosphere, plasma dynamics, ocean, optic fibers, signal processing, etc. In the circumstances of Saturn’s ring, it is noticed that the breather soliton structures are modified significantly with variations in dust charge concentration, ion temperature ratio, and other physical parameters.

Breathers for nonlinear energy management in acoustic waveguides

Recent investigations of nonlinear metamaterials have revealed interesting wave propagation phenomena with no counterpart in linear systems. One of the appealing phenomena is traveling discrete breathers. Breathers are traveling oscillatory wavepackets with spatially localized envelopes and energy-dependent speeds. These nonlinear waves were reported in lattices with purely (or nearly purely) nonlinear neighbor interactions (possessing zero speed of sound as defined in the classical acoustics sense, and, hence, designated as sonic vacua). However, the effect of local resonators on breather propagation is elusive to date. In this work, we aim to fill this gap by studying 1D grounded strongly nonlinear lattices with linear local resonators (SNLRMs) under impulsive force excitation. Numerical simulations have demonstrated that SNLRMs support the generation of new families of breathers. These families resulted from the opening of a new optical propagation zone (PZ) in the spectrum, which is associated with the linear dynamics of the local resonators. These families are characterized by the local resonator parameters and can support multiple fast frequencies or a single frequency that belongs to either the optical or acoustical PZs. Further aspects of the nonlinear acoustics are also demonstrated using the complexification averaging method. The newly reported breathers open the venue to employ SNLRMs in passive nonlinear energy management applications. Examples are presented through acoustics waveguides and frequency filtering.

Generation of super high frequencies by graphene on piezoelectric buffer layer upon applied nanosecond electrical pulse

An unforeseen phenomenon occurred when measuring the current–voltage (I–U) characteristics of graphene samples in the pulsed regime. The graphene monolayer of the samples was grown by chemical vapor deposition and transferred onto 50 nm buffer HfO2 and AlO3 layers. Bilayer graphene was obtained from epitaxial graphene grown on SiC and was transferred onto 100 nm SiO2. The distance between contacts varied from 5 to 25 µm. The measurements were performed employing cables of 50 Ω impedance to transmit the pulses and a 0–12 GHz bandwidth sampling scope was used to register them. The transmitted registered pulses through graphene/HfO2 and graphene/SiO2 samples were superposed with super high frequency (SHF) oscillations. The wave packet oscillations of about 2 ns in duration appeared on the pulses passed through graphene/HfO2. On the passed-through graphene/SiO2 pulses, the appearing wave packet turns into continuous generation along the pulse length. Spectral decomposition reveals that the base frequency of the oscillations is about 10 GHz; however, bisected frequencies are also present in the spectra. Preliminary analysis of the SHF oscillations occurrence shows that the wave packets appear as an inverse piezoelectric response to a rapidly rising voltage of the pulses. It is proposed that due to acoustic–electronic interaction, the oscillating wave packet in graphene/SiO2 turns into the continued generation, which consumes three-quarters of the pulse energy. These results show that the coupling between graphene and the piezoelectric buffer layer combined with acoustic–electronic interaction brings forth novel effects that are in demand for practical applications.

Bloch oscillations in moiré flat band systems

Bloch oscillations of wave packets in moiré flat band systems are investigated. We find that the real space trajectories and group velocity of wave packet undergo Bloch oscillations in the moiré flat band. It is shown that the Bloch dynamics is affected significantly by the magnitude and orientation of an applied in-plane electric field. In the presence of both external perpendicular magnetic field and in-plane electric field, confinement and de-confinement of cyclotron orbits occur which strongly depend on the relative strength of the applied fields.

Pendulum-type light beams

Nondiffracting and shape-preserving light beams have been extensively studied and were shown to exhibit intriguing wave phenomena, which led to applications including particle manipulation, curved plasma channel generation, and optical superresolution. However, these beams are generated by caustics, i.e., conical superposition of waves. As a result, they tend to propagate along a straight line or accelerate in a plane [(1 + 1)D], and tailoring their propagation trajectories in a higher dimension [(2 + 1]D] is challenging. Here we report both theoretically and experimentally a class of nondiffracting solutions to the paraxial wave equation perturbed by harmonic potential. We demonstrate that the initial wave packets of light can be engineered to accelerate along an arbitrary trajectory centered on an elliptic or a circular orbit in a (2 + 1)D configuration, while maintaining their phase and polarization structures during propagation. Such particle-like features manifested by orbital movements can be attributed to the centripetal force of the underlying potential. We name such oscillating wave packets as pendulum-type beams. We suggest the concept can be generalized to other waves such as quantum waves, matter waves, and acoustic waves, opening possibilities for the study and applications of the pendulum-type wave packet in a wide range, e.g., it may be utilized in the field of laser scanning technology.

Nonlinear Bloch dynamics and spin-wave generation in a Bose-Hubbard ladder subject to effective magnetic field.

The two-leg magnetic ladder is the simplest and ideal model to reflect the coupling effects of lattice and magnetic field. It is of great significance to study some novel phases, topological characteristics, and chiral characteristics in condensed matter physics. In particular, the left-right leg degree of freedom can be regarded as a pseudospin, and the two-leg magnetic ladder also provides an ideal platform for the study of spin dynamics. Here the ground state, Bloch oscillations (BOs), and spin dynamics of the interacting two-leg magnetic ladder subject to an external linear force are studied by using variational approach and numerical simulation. In the absence of the external linear force, the critical condition of transition between the zero-momentum state and plane-wave state is obtained analytically, and the physical mechanism of the ground-state transition is revealed. When the external linear force presents, the occurrence of BOs excites the spin dynamics, and we reveal the chiral BOs and the accompanied spin dynamics of the system in different ground states. In particular, we further study the influence of periodically modulated linear force on BOs and spin dynamics. The frequencies of the linear force corresponding to the resonances and pseudoresonances are obtained analytically, which result in rich nonlinear dynamics. In resonances, stable and strong BOs (with larger amplitude) are observed. In pseudoresonances, because the pseudoresonance frequencies are related to the initial momentum and phase of the wave packet, a dispersion effect takes place and strong diffusion of wave packet occurs. When the frequency is nonresonant, drift and weak dispersion of wave packet occur simultaneously with the wave-packet oscillation. In all cases, the wave-packet dynamics is accompanied with periodic but anharmonic pseudospin oscillation. The BOs and spin dynamics are effectively controlled by periodically modulating the linear force.

Plane-wave and wave-packet neutrino flavor oscillations in vacuum in conformal coupling models

We investigate neutrino flavor oscillations in vacuum within a general conformal coupling model. We first examine the flavor oscillations within the plane-wave description of neutrinos, and then we extend our analysis to the wave-packet-based formalism. In both cases, we derive the general formulas for the flavor transition probability in arbitrary static and spherically symmetric spacetimes. We thoroughly discuss and assess in both cases the different possible ways---dictated by the presence of the conformal coupling---of computing the flavor transition probability. We show that the conformal invariance of the Dirac equation implies that the effect of conformal coupling on neutrino flavor oscillations modifies the oscillation length but preserves the coherence length and unitarity. A detailed application to two-flavor neutrinos is then made, and a numerical analysis is conducted within the well-known chameleon conformal coupling model.

H-Theorem in an Isolated Quantum Harmonic Oscillator.

We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrödinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics.

On the exact revival of Morse oscillator wave packets

On the exact revival of Morse oscillator wave packets

Modulation Approximation of a 2-Fluid System in Plasma

A kind of 2-fluid system in plasmas describes rich plasma dynamics, including the interactions between the ion acoustic wave and the plasma body wave. In order to describe the evolution of the envelope of the small oscillating wave packet solution of the 2-fluid model, the nonlinear Schrödinger (NLS) equation was derived as a formal approximation equation with the multi-scale analysis method, and the uniform energy estimation of the error between the exact solution and the approximate solution to the 2-fluid model was given in the Sobolev space. The NLS approximation was finally proved strictly on the time-scale <inlineformula><texmath id="M2">\begin{document}$ {\cal{O}}(\epsilon^{-2})$\end{document}</texmath><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-43-0007_M2.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-43-0007_M2.png"></graphic></alternatives></inlineformula> .

Ultrafast Dynamics of a Solvatochromic Dye, Phenol Blue: Tautomerization and Coherent Wavepacket Oscillations

Femtosecond time-resolved transient absorption spectroscopy was performed for a nonfluorescent solvatochromic dye, phenol blue, N-(4-dimethylaminophenyl)-1,4-benzoquinoneimine, which exhibits ultrafast nonradiative decay due to its flexible molecular structure. By exciting the molecule in ethanol (EtOH) solution with two excitation wavelengths located at shorter- and longer-wavelength sides of the visible absorption band, we observed ultrafast nonradiative decay from the excited state, followed by spectral evolution in the ground state. The nonradiative decay in the subpicosecond range creates a vibrationally hot ground state with the lifetime in the picosecond range. Subsequently, a tautomer that absorbs at shorter wavelengths is produced from the hot state, which causes a red shift of the ground-state bleach (GSB). The tautomerization presumably involves twisting of the benzoquinoneimine moiety induced by the breaking of the hydrogen bond (H-bond) between the solute and the solvent molecules. The recombination of the H-bond occurs with a time constant of ∼30 ps, and the system returns to its original state. We also observed low-frequency coherent wavepacket oscillations that modulate the GSB with dephasing times similar to the excited-state lifetime.

Families of Solutions of Multitemporal Nonlinear Schrödinger PDE

The multitemporal nonlinear Schrödinger PDE (with oblique derivative) was stated for the first time in our research group as a universal amplitude equation which can be derived via a multiple scaling analysis in order to describe slow modulations of the envelope of a spatially and temporarily oscillating wave packet in space and multitime (an equation which governs the dynamics of solitons through meta-materials). Now we exploit some hypotheses in order to find important explicit families of exact solutions in all dimensions for the multitime nonlinear Schrödinger PDE with a multitemporal directional derivative term. Using quite effective methods, we discovered families of ODEs and PDEs whose solutions generate solutions of multitime nonlinear Schrödinger PDE. Each new construction involves a relatively small amount of intermediate calculations.

Wave redirection, localization, and non-reciprocity in a dissipative nonlinear lattice by macroscopic Landau–Zener tunneling: Experimental results

Nonlinear lattices and the nonlinear acoustics they support have a broad impact on shock and vibration mitigation, sound isolation, and acoustic logic devices. In this work, we experimentally study wave redirection, localization, and non-reciprocity in an asymmetric network of two nonlinear lattices with weak linear inter-lattice coupling. We report on the design, fabrication, and system identification of coupled lattices with essentially nonlinear next-neighbor intra-lattice coupling and on their unusual nonlinear acoustics. By weakly coupling the lattices and introducing structural disorder in one of them, we experimentally prove the realization of irreversible breather redirection between lattices governed by a macroscopic analog of the quantum Landau–Zener tunneling effect. In the experiments performed, the input energy is applied by impulse (broadband) excitation, and the resulting acoustical mechanism for wave redirection is in the form of propagating breathers, that is, localized oscillating wave packets formed by the synergy of nonlinearity and dispersion. Moreover, we study the non-reciprocal acoustics of the experimental lattice system by applying separate impulses at each of its four terminals and investigate the tunability with the energy of the resulting acoustic non-reciprocity by systematically varying the impulse intensity. The reported experimental results show that the weakly coupled, disordered, and nonlinear lattice system has wave tailoring properties that are tunable with energy. Altogether, the experimental results agree well with theoretical predictions reported in a companion work based on reduced-order numerical models and prove the efficacy of the system for applications, providing a path for applying these advanced concepts in future structures and devices.

Effect of pseudospin polarization on wave packet dynamics in graphene antidot lattices (GALs) in the presence of a normal magnetic field

We have investigated the role of pseudospin polarization in electron wave packet dynamics in pristine graphene and in a graphene antidot lattice subject to an external magnetic field. By employing Green’s function formalism, we show that the electron dynamics can be controlled by tuning pseudospin polarization. We find that in Landau quantized pristine graphene, both the propagation of an electron wave packet and Zitterbewegung oscillations strongly depend on pseudospin polarization. The electron wave packet is found to propagate in the direction of initial pseudospin polarization. We also show that, in this system, the propagation of an electron can be enhanced in any desired direction by carving a one-dimensional antidot lattice in that direction. The study suggests that a graphene antidot lattice can serve as a channel for electron transport with the possibility of tunability by means of pseudospin polarization, antidot potential, and applied normal magnetic field strength.

Interaction Features of Internal Wave Breathers in a Stratified Ocean

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.

Structure tracking of nuclear wave packet oscillations by femtosecond time-resolved X-ray absorption spectroscopy

Progress in technology in recent decades has brought not only huge leaps in our knowledge across many fields, but has also led to the development of new tools that help and support the pursuit of such knowledge. Spectroscopy, the study of the interaction between matter and electromagnetic radiation, is used in chemistry, physics, astronomy and other fields, and allows scientists to investigate the physical and electronic structure as well as composition of materials. A number of techniques, including X-ray spectroscopy, have been developed to detect and measure materials in this way. Dr Tetsuo Katayama, from the Japan Synchrotron Radiation Research Institute (JASRI), is part of a team furthering research in this field.

Topological Swing of Bloch Oscillations in Quantum Walks.

We report new oscillations of wave packets in quantum walks subjected to electric fields, that decorate the usual Bloch-Zener oscillations of insulators. The number of turning points (or suboscillations) within one Bloch period of these oscillations is found to be governed by the winding of the quasienergy spectrum. Thus, this provides a new physical manifestation of a topological property of periodically driven systems that can be probed experimentally. Our model, based on an oriented scattering network, is readily implementable in photonic and cold atomic setups.

Vibrational decoherence induced by ultrafast intramolecular charge separation of an asymmetric bianthryl derivative.

Coherent wavepacket oscillation accompanying the ultrafast photoexcited intramolecular charge separation (CS) of 9,9'-bianthryl (BA) and 10-cyano-9,9'-bianthryl (CBA) in a room temperature ionic liquid, N,N-diethyl-N-methyl-N-(methoxyethyl)ammonium tetrafluoroborate (DemeBF4), was investigated by femtosecond time-resolved transient absorption spectroscopy. The frequency of the coherent oscillation observed for CBA in nonpolar n-hexane solution (Hex) was 377 cm-1, while this oscillation was undetectable in DemeBF4. For BA in DemeBF4, coherent oscillation with a frequency of 394 cm-1 was observed, which is similar to that for CBA in Hex. CS of CBA occurs in the ultrashort time range of ≤100 fs, while that of BA occurs in a few picosecond range [E. Takeuchi et al., J. Phys. Chem. C 120, 14502-14512 (2016)]. Hence, the oscillation of CBA in Hex and that of BA in DemeBF4 are assigned to the molecular vibration in the locally excited state, while this oscillation dephases instantaneously for CBA in DemeBF4 due to the ultrafast CS and no oscillation was generated in the CS state. This result suggests that the CS reaction is not mediated by a specific intramolecular vibration in the CS state but occurs incoherently through higher levels of multiple vibrational modes.

Zitterbewegung-mediated RKKY coupling in topological insulator thin films

The dynamics of itinerant electrons in topological insulator (TI) thin films is investigated using a multi-band decomposition approach. We show that the electron trajectory in the 2D film is anisotropic and confined within a characteristic region. Remarkably, the confinement and anisotropy of the electron trajectory are associated with the topological phase transition of the TI system, which can be controlled by tuning the film thickness and/or applying an in-plane magnetic field. Moreover, persistent electron wavepacket oscillation can be achieved in the TI thin film system at the phase transition point, which may assist in the experimental detection of the jitter motion (Zitterbewegung). The implications of the microscopic picture of electron motion in explaining other transport-related effects, e.g., electron-mediated RKKY coupling in the TI thin film system, are also discussed.

Transformation of first mode breather of internal waves above the bottom step in a three-layer fluid

In the present study we consider propagation of a localized internal perturbation in the form of an oscillating wave packet (breather) of the first mode in a three-layer fluid with an uneven bottom shaped as a smoothed step. The study is carried out by methods of numerical simulation within a fully nonlinear two-dimensional (vertical plane) set of NavierStokes equations. A set of calculations was carried out for different widths and heights of the bottom step. Inhomogeneity of the medium leads to transformation of the internal wave field with the formation of weak reflected waves and one or two first-mode breathers passed to the shallow zone. By analyzing linear stability in terms of Richardson and Froude numbers, it was revealed that potentially unstable regions arise at the smallest values of the step width. An amplitude and energy analysis of secondary reflected nonlinear waves was performed. The vertical mode composition of the fully nonlinear wave field is analyzed. It is shown that the first mode makes the largest contribution to the vertical structure of the full-nonlinear packet, though the fourth, second and the third modes also contribute noticeably.