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Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system's dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system–bath interactions, where a large number of degrees of freedom must be explicitly considered. [ABSTRACT FROM AUTHOR]

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 ab initio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the ab initio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study. [ABSTRACT FROM AUTHOR]

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 ab initio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the ab initio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study. [ABSTRACT FROM AUTHOR]

The quantum nuclear kinematic interactions with electrons (or nonadiabatic interactions) are the inherent driving force that possibly causes a mixture of the adiabatic electronic states in molecules. Particularly in systems whose electron wavepackets lie in a densely quasi-degenerate electronic-state manifold where many-dimensional and many-state nonadiabatic interactions last continually, we have found before that those extensive mixings can lead to a quantum electronic-state chaos [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 159, 074110 (2023)]. This chaos of electron dynamics is a new kind yet generic. This Communication identifies the mathematical/physical mechanism of this class of chaos by means of the collective coordinate analysis of the nonadiabatic interactions, along with the numerical applications to excited states of boron clusters. Some physical consequences of the present chaos are also discussed. [ABSTRACT FROM AUTHOR]

We present a concept for selective excitation of magnetostatic surface waves with a quasi-discrete spectrum using spatially patterned femtosecond laser pulses inducing either an ultrafast change of magnetic anisotropy or an inverse Faraday effect. We micromagnetically simulate the excitation of the waves with a periodically patterned uni- or bipolar laser impact. Such excitation yields multiple wavepackets propagating with different group velocities, whose dispersion corresponds to the set of quasi-discrete points. In addition, we show that the frequency of the spectral peaks can be controlled by the polarity of the periodic impact and its spatial period. The presented consideration of multiple spatially periodic magnetostatic surface wave sources as a whole enables implementation of a comprehensive toolkit of spatiotemporal optical methods for tunable excitation and control of spin-wave parameters. [ABSTRACT FROM AUTHOR]

Investigating the phonon-surface scattering mechanism is essential for the evaluation of thermal transport in nanostructures. The theoretical description to quantify this mechanism remains to be developed at the atomic scale. This work presents a phonon wave packet method to study the phonon-surface scattering behavior at rough surfaces. We obtain the specularity distribution dependent on phonon polarization, wavelength, and surface roughness. The reflection of the diffuse wave packet is primarily attributed to the surface shadowing effect at a higher incident angle, surface disorder, and surface-induced localized modes. Taking the wavevector-dependent specularity data as input, the thermal conductivity of silicon nanowires is calculated based on the Boltzmann Transport Equation. Our specularity model provides an accurate evaluation for predicting thermal conductivity. This work offers an atomic-level analysis for phonon-surface interaction, which is helpful for the understanding of thermal transport in nanostructures. [ABSTRACT FROM AUTHOR]

We tested and compared the stability and usability of three different cathode materials and configurations in a thermionic-based ultrafast electron microscope: (1) on-axis thermionic and photoemission from a custom 100 μm diameter LaB6 source with a graphite guard ring, (2) off-axis photoemission from the Ni aperture surface of the Wehnelt electrode, and (3) on-axis thermionic and photoemission from a custom 200 μm diameter polycrystalline Ta source. For each cathode type and configuration, including the Ni Wehnelt aperture, we illustrate how the photoelectron beam-current stability is deleteriously impacted by simultaneous cooling of the source following thermionic heating. Furthermore, we demonstrate usability via collection of parallel- and convergent-beam electron diffraction patterns and by formation of the optimum probe size. We find that usability of the off-axis Ni Wehnelt-aperture photoemission is at least comparable to on-axis LaB6 thermionic emission, as well as to on-axis photoemission [the heretofore conventional approach to ultrafast electron microscopy (UEM) in thermionic-based instruments]. However, the stability and achievable beam currents for off-axis photoemission from the Wehnelt aperture were superior to that of the other cathode types and configurations, regardless of the electron-emission mechanism. Beam-current stability for this configuration was found to be ±1% (one standard deviation from the mean) for 70 min (longest duration tested), and steady-state beam current was reached within the sampling-time resolution used here (∼1 s) for 15 pA beam currents (i.e., 460 electrons per packet for a 200 kHz repetition rate). Repeatability and robustness of the steady-state condition were also found to be within ±1% of the mean. We discuss the implications of these findings for UEM imaging and diffraction experiments, for pulsed-beam damage measurements, and for practical switching between optimum conventional TEM and UEM operation within the same instrument. [ABSTRACT FROM AUTHOR]

C H 3 + , a cornerstone intermediate in interstellar chemistry, has recently been detected for the first time by using the James Webb Space Telescope. The photodissociation of this ion is studied here. Accurate explicitly correlated multi-reference configuration interaction ab initio calculations are done, and full-dimensional potential energy surfaces are developed for the three lower electronic states, with a fundamental invariant neural network method. The photodissociation cross section is calculated using a full-dimensional quantum wave packet method in heliocentric Radau coordinates. The wave packet is represented in angular and radial grids, allowing us to reduce the number of points physically accessible, requiring to push up the spurious states appearing when evaluating the angular kinetic terms, through projection technique. The photodissociation spectra, when employed in astrochemical models to simulate the conditions of the Orion bar, result in a lesser destruction of C H 3 + compared to that obtained when utilizing the recommended values in the kinetic database for astrochemistry. [ABSTRACT FROM AUTHOR]

Stereodynamics is a field that studies the influence of the alignment or orientation of colliding partners on the results of collisions. At present, the intersection of nonadiabatic effects and stereodynamics remains to be explored. In this study, we theoretically demonstrate significant stereodynamical effects in the D + HD (v = 1, j = 2) → D2 + H reaction within the collision energy range of 0.01–2.99 eV by using the time-dependent wave packet method. It is found that the stereodynamical control not only facilitates the reaction but also allows precise control of the products over a range of different scattering angles. The analysis at the state-to-state level reveals that the nonadiabatic effects are stronger in the parallel configuration than in the perpendicular configuration. By topological approach to separate the two reaction pathways at the conical intersection, the scattering amplitude of the roaming pathway in the parallel configuration is larger than that of the perpendicular configuration, which leads to more dramatic nonadiabatic features in the collision with parallel configuration. [ABSTRACT FROM AUTHOR]

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment–protein complexes. [ABSTRACT FROM AUTHOR]

Using non-equilibrium molecular dynamics simulations, we investigate thermal transport in organic/inorganic Au/molecular nanolayer (MNL) nanolaminate. We examine the tunability of thermal conductivity via interfacial bonding by (i) homogeneous change of bonding strength and heterogeneous change of (ii) bond density and (iii) molecular coverage at the interface. By comparing the thermal conductivity of the nanolaminates with the interfacial thermal conductance of corresponding individual interfaces, we conclude that phenomenologically the thermal conductivity can be predicted from independent interfacial resistors connected in a series model, particularly at higher temperatures. However, interfacial thermal conductance shows a moderate increase with temperature, whereas the thermal conductivity of Au/MNL nanolaminates shows the opposite effect. We elucidate this apparent contradiction via phonon wave packet simulations at individual and multiple interface structures. [ABSTRACT FROM AUTHOR]

The vibronic structure and nuclear dynamics in the first five excited singlet electronic states of bithiophene (2T) are investigated here. Specifically, considerations are given to comprehend the first two structureless and broad electronic absorption bands and the role of nonadiabatic coupling in the excited state relaxation mechanism of 2T in the gas phase. Associated potential energy surfaces (PESs) are established by constructing a model vibronic coupling Hamiltonian using 18 vibrational degrees of freedom and extensive ab initio electronic structure calculations. The topographies of these PESs are critically examined, and multiple conical intersections are established. The nuclear dynamics calculations are performed by propagating wave packets on the coupled electronic manifold. The present theoretical results are in good agreement with the experimental observations. It is found that strong nonadiabatic coupling between the S1–S4 and S1–S5 states along totally symmetric modes is predominantly responsible for the structureless and broad first absorption band, and overlapping S2, S3, S4, and S5 states form the second absorption band. Photorelaxation from the highly excited S5 to the lowest S1 state takes place through a cascade of diabatic population transfers among the S1–S4–S5 electronic manifold within the first ∼100 fs. Totally symmetric C=C stretching, C–S stretching, C–H wagging, ring puckering, and inter-ring bending modes collectively drive such relaxation dynamics. [ABSTRACT FROM AUTHOR]

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4–9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra. [ABSTRACT FROM AUTHOR]

The barrierless exothermic reactions between atomic oxygen and the cyano radical, O(3P) + CN(X2 Σ + ) → CO(X1Σ+) + N(2D)/N(4S), play a significant role in combustion, astrochemistry, and hypersonic environments. In this work, their dynamics and kinetics are investigated using both wave packet (WP) and quasi-classical trajectory (QCT) methods on recently developed potential energy surfaces of the 12A′, 12A,″ and 14A″ states. The product state distributions in the doublet pathway obtained with the WP method for a few partial waves show extensive internal excitation in the CO product. This observation, combined with highly oscillatory reaction probabilities, signals a complex-forming mechanism. The statistical nature of the reaction is confirmed by comparing the WP results with those from phase space theory. The calculated rate coefficients using the WP (with a J-shifting approximation) and QCT methods exhibit agreement with each other near room temperature, 1.77 × 10−10 and 1.31 × 10−10 cm3 molecule−1 s−1, but both are higher than the existing experimental results. The contribution of the quartet pathway is small at room temperature due to a small entrance channel bottleneck. The QCT rate coefficients are further compared with experimental results above 3000 K, and the agreement is excellent. [ABSTRACT FROM AUTHOR]

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree–Fock with spin–orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born–Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results. [ABSTRACT FROM AUTHOR]

The 6D time-dependent wave packet calculations were performed to explore H2 dissociation on Ag, Au, and two AgAu alloy surfaces, using four newly fitted potential energy surfaces based on the neural network fitting to density functional theory energy points. The ligand effect resulting from the Ag–Au interaction causes a reduction in the barrier height for H2+Ag/Au(111) compared to H2+Ag(111). However, the scenario is reversed for H2+Au/Ag(111) and H2+Au(111). The 6D dissociation probabilities of H2 on Ag/Au(111) surfaces are significantly higher than those on the pure Ag(111) surface, but the corresponding results for H2 on Au/Ag(111) surfaces are substantially lower than those on the pure Au(111) surface. The reactivity of H2 on Au(111) is larger than that on Ag(111), despite Ag(111) having a slightly lower static barrier height. This can be attributed to the exceptionally small dissociation probabilities at the hcp and fcc regions, which are at least 100 times smaller compared to those at the bridge or top site for H2+Ag(111). Due to the late barrier being more pronounced, the vibrational excitation of H2 on Ag(111) is more effective in promoting the reaction than on Au(111). Moreover, a high degree of alignment dependence is detected for the four reactions, where the H2 dissociation has the highest probability at the helicopter alignment, as opposed to the cartwheel alignment. [ABSTRACT FROM AUTHOR]

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x - and y -components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

Solving the Liouville–von-Neumann equation using a density operator provides a more complete picture of dynamical quantum phenomena than by using a wavepacket and solving the Schrödinger equation. As density operators are not restricted to the description of pure states, they can treat both thermalized and open systems. In practice, however, they are rarely used to study molecular systems as the computational resources required are even more prohibitive than those needed for wavepacket dynamics. In this paper, we demonstrate the potential utility of a scheme based on the powerful multi-layer multi-configurational time-dependent Hartree algorithm for propagating multi-dimensional density operators. Studies of two systems using this method are presented at a range of temperatures and including up to 13 degrees of freedom. The first case is single proton transfer in salicylaldimine, while the second is double proton transfer in porphycene. A comparison is also made with the approach of using stochastic wavepackets. [ABSTRACT FROM AUTHOR]

In this paper, the optical soliton and solitary wave solutions of the (2 + 1) -dimensional Mel'nikov equation are investigated using the Kudryashov R function technique. The Kudryashov R function approach has various features that significantly facilitate symbolic computing, particularly for highly dispersive nonlinear equations. In computations, this approach has the benefit of not requiring the use of a certain function form. This approach gives an algorithm that is straightforward, efficient, and simple for finding solitary wave solutions. In addition, this approach is very influential and reliable when it comes to discovering hyperbolic function solutions of nonlinear equations. Many new hyperbolic function solutions have been obtained from the governing equation by using this technique. In addition, numerous types of soliton solutions describing various structures of optical solitons are retrieved. Using this method, breather, W-shaped, bell shaped, and bright soliton solutions have been generated from the governing equation. From the obtained results, it can be asserted that the applied approach may be a useful tool for addressing more highly nonlinear problems in various fields. By choosing particular values for the relevant parameters, the dynamic features of some breather, W-shaped, bell shaped and bright soliton solutions to the (2 + 1) -dimensional Mel'nikov equation have been displayed in 3D, 2D and contour graphs. [ABSTRACT FROM AUTHOR]

Strong similarities for relativistic electrons stimulated from electron beams and electron clouds are merging the boundary of wave‐particle duality of electrons, one of which being superposition is Cherenkov radiations. Recent theoretical investigations into quantum Cherenkov effects for cone‐shape particles have hypothesized electron‐spin flip transitions in bound‐ and free‐electron systems like bulk silica and graphene. However, experimental validation of these predictions remains outstanding. Here, analogous phenomena of polariton‐version quantum Cherenkov radiations observed by broadband femtosecond pump‐probe experiments is reported, and demonstrate double‐cone emission processes involving of Cherenkov‐type phonon polaritons (PhPs) and plasmon‐PhPs in ultrashort‐pulse‐stimulated ferroelectric crystals and graphene, respectively. Through component analysis of double‐cone polariton emissions using an empirical quantum dynamics model, the initial polariton dynamics are restored by time translation corrections. The resulting quantum wave packets of PhPs are found to be correlated with femtosecond‐laser‐induced modifications inside ferroelectric lithium niobates, achieving a PhP threshold criterion for ultrasmooth femtosecond laser nanofabrication. [ABSTRACT FROM AUTHOR]

Wave trains of magnetic field and ion-flux oscillations generated upstream of the ramp of interplanetary (IP) shock were studied according to BMSW plasma-spectrometer measurements of energy–time spectra of the solar-wind ions supplemented by magnetic-field measurements. It was shown that oscillations of the magnetic field upstream of the ramp of IP shock are accompanied by oscillations of the ion flux. A detailed analysis of two cases is carried out, and the results of statistical study are presented. Right-handed circular or elliptical polarization was observed in all wave trains of magnetic-field oscillations, which is consistent with the characteristics of magnetosonic oscillations corresponding to the low-frequency branch of whistler waves. It was obtained that the mean angles between the propagation direction of whistler waves relative to the magnetic field and shock normal direction were 31° and 40°, respectively. This result suggests that the wave packets upstream of the ramp of IP shock had the properties of propagating whistler waves. It was found that, on average, with an increase in the angle of propagation of whistler waved relative to the shock normal direction θkn, the angle between the wave vector and magnetic-field direction θkB decreases. [ABSTRACT FROM AUTHOR]

We develop a multilayer model to study roll waves in mudflow of Herschel–Bulkley fluids initiated by periodic and localized disturbance. Simulations are conducted of the temporal development of periodic roll waves and spatial development of wave packets due to localized disturbance. The results of the temporal development are expressed in terms of the power-law index, the relative plug-layer thickness, the Froude number, and the perturbation wavelength. Our simulation for the spatial development shows the roll waves led by a dominant front runner and followed by a quiescent tail, closely reproducing a well-known river-clogging phenomenon of the natural mudflow observed in the mountain rivers on mild slopes. The leading wave of the roll-wave packet, i.e., the front runner, grows in depth, velocity, celerity, and wavelength with distance from the localized disturbance. The front-runner wave amplitude depends on the distance from the localized disturbance, the power law index, the plug-layer thickness, and the Froude number. We calculated the front-runner's wave amplitude due to a line source of disturbance in a 1D unidirectional development and the roll waves' 2D development due to a point source. The initial nonlinear growth in the 2D front runner is a fraction of the 1D waves, but the increase in the wave amplitude with distance follows the same trend. We have also conducted a mesh refinement study to determine the convergence and accuracy. The present simulations using 64 layers have attained an accuracy within a 2% error. [ABSTRACT FROM AUTHOR]

The free metaplectic transformation (FMT) is an n$$ n $$‐dimensional linear canonical transform. This transform is much useful, especially in multidimensional signal processing and applications. In this paper, our aim is to achieve an efficient time‐frequency representation of higher‐dimensional nonstationary signals by introducing the novel free metaplectic wave packet transform (FM‐WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$, based on the elegant convolution structure associated with the free metaplectic transforms. The FM‐WPT preserves the properties of classical wave packet transform (WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$ and has better mathematical properties. Further, the validity of the proposed transform is demonstrated via a lucid example. The preliminary analysis encompasses the derivation of fundamental properties of the novel FM‐WPT, including boundedness, reconstruction formula, Moyal's formula, and the reproducing kernel. To extend the scope of the study, we formulate several uncertainty inequalities, including Lieb's inequality, Pitt's inequality, logarithmic inequality, Heisenberg's uncertainty inequality, and Nazarov's uncertainty inequality for the proposed transform. [ABSTRACT FROM AUTHOR]

The time delay in strong field tunneling ionization presents a captivating challenge in the field of attoscience. It is linked to the phase of the photoelectron wavepacket, a relationship that modern attosecond photoelectron interferometry can effectively probe. However, the connection between sub-barrier dynamics and the phase formation remains unclear. In this study, we investigate the role of under-the-barrier recollisions for shaping the phase of the photoelectron wavepacket. We establish a general analytical relationship between the phase of the tunneled electron wavepacket and the tunneling rate. Our results demonstrate that the Coulomb field effect of the atomic potential enhances both the amplitude of the recolliding path and the phase shift of the wavepacket, effectively countering the lateral spreading of the tunneling wavepacket during sub-barrier propagation. The insights gained from this research will aid in the development of free electron wavepackets with tailored properties through strong field ionization. This work investigates the origin of time delay in strong field tunneling ionization and its relation to the parameters of the photoelectron wavepacket. The authors establish a general analytical relationship between the phase of the wavepacket and the tunneling rate, and analyze the role of under-the-barrier recollisions for shaping the photoelectron wavepacket. [ABSTRACT FROM AUTHOR]

The (generalized) Derivative Nonlinear Schrödinger (DNLS) equation can be derived as an envelope equation via multiple scaling perturbation analysis from dispersive wave systems. It occurs when the cubic coefficient for the associated NLS equation vanishes for the spatial wave number of the underlying slowly modulated wave packet. It is the purpose of this paper to prove that the DNLS equation makes correct predictions about the dynamics of a Klein-Gordon model with a cubic nonlinearity. The proof is based on energy estimates and normal form transformations. New difficulties occur due to a total resonance and due to a second order resonance. [ABSTRACT FROM AUTHOR]

The relationship between total solar irradiance (TSI) forcing and summer extreme precipitation and flood frequency over western Europe is investigated from a synoptic‐scale perspective, with a focus on the role of Rossby wave packets (RWPs). Utilizing observational, model, and proxy data, we reveal a significant increase in RWP frequency along a zonal band centered around 50°N, extending from North America to western Europe, during periods of low TSI. This anomaly in RWP frequency is consistent with a significant increase in the frequency of extreme precipitation events recorded over western Europe. Sensitivity experiments conducted with a state‐of‐the‐art chemistry‐climate model corroborate our findings based on observational data. Additionally, a flood record from western Europe demonstrates a significant increase in flood frequency during low TSI years, a relationship that persists across timescales. We argue that the frequency patterns associated with TSI forcing presented in this study are robust and, therefore, valuable for estimating the frequency of extreme precipitation events over western Europe under various solar irradiance scenarios. Moreover, our findings indicate that the North Atlantic sector is more responsive to changes in solar forcing during the boreal summer than previously thought, with this effect manifesting primarily on synoptic timescales rather than the long‐term climatological mean. Plain Language Summary: The total solar irradiance change has a significant impact on precipitation extremes over western Europe. Based on statistical analysis of observed and reconstructed data, we show that during low total solar irradiance years the frequency of extreme precipitation and floods over western Europe is significantly higher than the climatology due to more frequent synoptic‐scale Rossby wave packet (RWP) events. Analysis of paleoclimate data reveals similar relationships between total solar irradiance forcing and RWP and extreme precipitation frequency for different timescales. We argue that the RWP patterns presented here are useful to estimate the evolution of extreme precipitation and floods over western Europe during the next decades/centuries under different solar irradiance scenarios. Key Points: Low solar irradiance is associated with more frequent Rossby wave packets and extreme precipitation over western Europe during summer.Paleoclimate data suggests that these links are robust across different timescales.In the scenario of decreasing solar irradiance during next decades/centuries, an increase in Sun‐related precipitation extremes is expected. [ABSTRACT FROM AUTHOR]

At present, researchers in the field of pipeline inspection focus on pipe wall defects while neglecting pipeline defects in special situations such as welds. This poses a threat to the safe operation of projects. In this paper, a multi-node fusion and modal projection algorithm of steel pipes based on guided wave technology is proposed. Through an ANSYS numerical simulation, research is conducted to achieve the identification, localization, and quantification of axial cracks on the surface of straight pipelines and internal cracks in circumferential welds. The propagation characteristics and vibration law of ultrasonic guided waves are theoretically solved by the semi-analytical finite element method in the pipeline. The model section is discretized in one-dimensional polar coordinates to obtain the dispersion curve of the steel pipe. The T(0,1) mode, which is modulated by the Hanning window, is selected to simulate the axial crack of the pipeline and the L(0,2) mode to simulate the crack in the weld, and the correctness of the dispersion curve is verified. The results show that the T(0,1) and L(0,2) modes are successfully excited, and they are sensitive to axial and circumferential cracks. The time–frequency diagram of wavelet transform and the time domain diagram of the crack signal of Hilbert transform are used to identify the echo signal. The first wave packet peak point and group velocity are used to locate the crack. The pure signal of the crack is extracted from the simulation data, and the variation law between the reflection coefficient and the circumferential and radial dimensions of the defect is calculated to evaluate the size of the defect. This provides a new and feasible method for steel pipe defect detection. [ABSTRACT FROM AUTHOR]

Non-invasive diagnostic modalities are integral to cardiovascular care; however, current systems primarily measure peripheral pressure, limiting the breadth of cardiovascular prognostication. We report a novel approach for extracting left side heart sounds using a brachial cuff device. The technique leverages brachial cuff device enhanced signal resolution to capture pressure fluctuations generated by cardiohemic system vibrations, the sound pressure waveform. We analyze left heart catheterization data alongside simultaneous brachial cuff device measurements to correlate sound pressure waveform features with left ventricle (LV) contractility. The extracted sound pressure waveform reveals two prominent oscillatory wave packets, termed WP1 and WP2, originating from cardiac structure vibrations associated with LV contractions and relaxation. We demonstrate that WP1 originates from LV contraction during systolic blood ejection through the aortic valve (AV) and is correlated with LV isovolumetric contraction, clinically measured by LV dPdt-max (Pearson-R = 0.65, p < 0.001). Additionally, we show that WP2 comes from LV elongation required for blood flow deceleration at the end of systole, causing AV closure, and is correlated with LV isovolumetric relaxation, measured by LV ndPdt-max (Pearson-R = 0.55, p < 0.001). These findings highlight the value of cuff sound pressure waveforms in providing insights about dynamic coupling of the LV-Aorta complex for non-invasive assessment of LV contractility. [ABSTRACT FROM AUTHOR]

We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic evolution of the large-scale background wave so that these equations have an additional integral of motion. This condition is expressed mathematically as a system of equations for the carrier wave number as a function of the background variables. We show that a solution of this system for a given dispersion relation of linear waves is related to the quasiclassical limit of the Lax pair for the completely integrable equation having the corresponding dispersionless and linear dispersive behavior. We illustrate the theory with several examples. [ABSTRACT FROM AUTHOR]

We report a variational formalism to calculate how much free energy can be released in a drift wave turbulence system, through which estimating the upper limit of the zonal flow intensity becomes possible. This formalism is rooted in the same structure between the wave kinetic equation and the particle kinetic equation, i.e., both following a Liouville equation. The minimal energy state is approached by rearranging the "quasi-particles" (i.e., wave packets) in their phase space. Taking the Charney–Hasegawa–Mima system as a prototype, we analytically derived an upper limit of the available free energy for a Gaussian initial distribution of the wave action. For more general scenarios, by developing an algorithm of rearrangement, we numerically calculated the available free energy. Through direct numerical simulations, it is further verified that the total energy of the zonal flow does not exceed the upper bound set by the variational principle. [ABSTRACT FROM AUTHOR]

Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These phenomena, well known in optics and condensed matter physics, are referred to as spin Hall effects. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will have profound implications for astrophysics and tests of general relativity. [ABSTRACT FROM AUTHOR]

We introduce a simplified model for wave turbulence theory—the Wick nonlinear Schrödinger equation, of which the main feature is the absence of all self‐interactions in the correlation expansions of its solutions. For this model, we derive several wave kinetic equations that govern the effective statistical behavior of its solutions in various regimes. In the homogeneous setting, where the initial correlation is translation invariant, we obtain a wave kinetic equation similar to the one predicted by the formal theory. In the inhomogeneous setting, we obtain a wave kinetic equation that describes the statistical behavior of the wavepackets of the solutions, accounting for both the transport of wavepackets and collisions among them. Another wave kinetic equation, which seems new in the literature, also appears in a certain scaling regime of this setting and provides a more refined collision picture. [ABSTRACT FROM AUTHOR]

Quantum information processors benefit from high clock frequencies to fully harness quantum advantages before they are lost to decoherence. All-optical systems offer unique benefits due to their inherent 100-THz carrier frequency, enabling the development of THz-clock frequency processors. However, the bandwidth of quantum light sources and measurement devices has been limited to the MHz range, with nonclassical state generation rates in the kHz range. In this study, we demonstrated broadband generation and quantum tomography of non-Gaussian states using an optical parametric amplifier (OPA) as a squeezed light source and an optical phase-sensitive amplifier (PSA). Our system includes a 6-THz squeezed-light source, a 6-THz PSA, and a 66-GHz homodyne detector. We successfully generated non-Gaussian states at a 0.9 MHz rate with sub-nanosecond wave packets using a continuous-wave laser. The performance is currently limited by the jitter of superconducting detectors, restricting the usable bandwidth to 1 GHz. Our technique extends the bandwidth to GHz, potentially increasing non-Gaussian state generation rates for practical optical quantum processors using OPAs. The use of optical phase sensitive amplifiers (PSA) has been shown to allow fast quantum tomography of Gaussian states, but non-Gaussian states are a key component for quantum computation using optical continuous-variable systems. Here, the authors extend PSA-enhanced high-bandwidth homodyne detection to non-Gaussian states. [ABSTRACT FROM AUTHOR]

Bolt loosening in bolted lap-joint connections can result in catastrophic failures in industrial settings. Therefore, it is crucial to investigate these connections thoroughly and implement preventative measures. However, examining such connections requires considering multiple influencing parameters. In this study, numerical simulations were conducted using three-dimensional finite element analysis in Abaqus software to evaluate these parameters in detail. The study employed a guided wave-based structural health monitoring approach and a precise ultrasonic-guided Lamb wave propagation method. Time signals were analyzed using phase shift and transmission coefficient (TC) factors as suitable indicators. Additionally, the S0 mode of the captured waves provided a highly informative wave packet for analysis due to its specific order. Initially, various simulations were carried out to determine the optimal length of the overlapping region that would result in the most effective transmission of waves. Increasing the bolt torque and the contact friction coefficient between the two plates in the overlapping region reduces the time for waves to reach the sensor and increases the TC of the passing waves. However, the saturation state does not cause any change in the received signals. Increasing the bolt torque is more effective in facilitating wave transmission through the connections than increasing the contact friction coefficient. Furthermore, variations in excitation voltage do not affect the arrival time or TC of the waves. The continuous wavelet transformation enabled a more detailed time-frequency analysis. The results demonstrate that changes in bolt torque do not impact the wave frequencies reaching the sensors, making the frequency insensitive to bolt loosening. Ultimately, the numerical simulation results were validated through experiments on a table-top laboratory sample. This research enhances researchers' understanding of monitoring the health status of bolted lap-joint connections by investigating the impact of various parameters on guided Lamb wave transmission through these connections. [ABSTRACT FROM AUTHOR]

This compilation represents a summary of the main physical foundations underlying the structure and properties of spatiotemporal optical vortices (STOVs). The general approach to the STOV description and characterization is based on the model of a scalar paraxial Gaussian wave packet. On this ground, the STOV structures of arbitrary orders are considered as superpositions of spatiotemporal Hermite–Gaussian modes. This approach enables a systematic characterization of the main STOV properties in an explicit and physically transparent form. In particular, we analyze the STOV amplitude and phase distributions, their evolution upon free propagation and in optical systems, internal energy flows and the orbital angular momentum. The topologically determined inherent asymmetry of the STOVs and the difference between the "energy center" and "probability center" [K. Bliokh, Phys. Rev. A 107, L031501 (2023)] are discussed and qualitatively interpreted. Methods for the STOV generation and diagnostics are outlined, and the main properties of non-Gaussian (Bessel-type) STOVs are briefly described. Finally, limitations of the scalar Gaussian model, accepted throughout the whole text, are considered, and possible generalizations are exposed. The whole presentation may be useful as an initial introduction to the STOV-associated ideas and their extraordinary properties. [ABSTRACT FROM AUTHOR]

The terrestrial bow shock is the boundary where supersonic solar wind slows down abruptly near the magnetopause. The shock front geometry could be modulated by surface waves to form rippled structures, which impact the acceleration process of the solar wind particles. However, the rippled structures are hard to be identified unambiguously due to the similar signatures in single‐spacecraft observations between rippled shocks and reforming shocks. Here, we utilize the four‐spacecraft observations from the MMS mission to investigate an event of quasi‐perpendicular bow shock crossing. The periodic oscillations of shock normal directions and normal velocities support the scenario of surface wave propagation in the tangential direction. We also reconstruct the shock profile along the normal direction, and its monotonic shape further excludes the occurrence of shock reformation. These ripples are found to modulate the reflected ions and whistler wave packets, which adds to the complexity of the bow shock plasma environments. Plain Language Summary: Collisionless shocks are ubiquitous structures in the space and astrophysical plasma environments where significant energy conversion occurs between electromagnetic energy, kinetic energy, and thermal energy. These structures often exhibit nonstationary signatures, from which important information on the associated plasma dynamics can be extracted. In this paper, we report the spacecraft observations of a bow shock crossing with periodic enhancements of the magnetic field strength. Such signatures have been previously attributed either to the rippled shock structures or to the shock reformation process. These two potential processes are examined via simultaneous observations at four different locations, which shows the periodic oscillations of the local shock normal directions indicative of rippled rather than reforming shocks. We also show that the rippled shocks could spatially modulate the reflected ions and whistler wave packets, so they can also be detected periodically by the spacecraft. This phenomenon has been reported on other planets across a wide range of Mach numbers, indicating that the shock ripples, universal in the plasma universe, play a critical role in impacting particle dynamics and shock evolution processes. Key Points: Periodic magnetic strength enhancements are observed during the bow shock crossing of the MMS spacecraftMulti‐spacecraft analysis supports the scenario of shock ripples rather than the shock reformation processThe surface waves alter the shock geometry, modulating the reflected ions and whistler wave packets [ABSTRACT FROM AUTHOR]

The fundamental shear horizontal (SH0) guided wave transducer shows unique promise for non-destructive testing and structural health monitoring in oil pipelines, railway tracks, solar power plants, and beyond due to its non-dispersive characteristics. Under this background, it is desirable to explore the high-performance piezoelectric crystals to develop the SH0 guided wave transducers. Herein, a novel piezoelectric crystal KCsMoP2O9 (KCMP) with dominant face shear mode d14 was grown by Kyropoulos method and proposed to excite and receive the SH0 wave based on the finite element simulation. The resonance frequency was found to be 190 kHz with the designed size of 6 mm × 6 mm × 1.5 mm. The group velocity of generated wave packet was determined to be 3040 m/s, affirming that the detected signal was the SH0 wave. The simulated and experimental results demonstrated the exceptional ability of KCMP-based guided wave transducer to generate and detect obvious SH0 waves in two orthogonal principal directions over a wide frequency range (160–360 kHz). Additionally, the KCMP-based SH0 wave transducer showcases its excellent defect localization ability with high signal-to-noise ratio (~ 30 dB), demonstrating its great potential for application in non-destructive testing and structural health monitoring. [ABSTRACT FROM AUTHOR]

Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a "Schrodinger kink" that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics. [ABSTRACT FROM AUTHOR]

The commonly used baseline-free Lamb wave damage identification methods often require a large amount of sensor data to eliminate the dependence on baseline signals. To improve the efficiency of damage localization, this paper proposes a new Lamb wave damage location method, namely the probabilistic exchanging-element time-reversal method (PEX-TRM), which is based on the exchanging-element time-reversal method (EX-TRM) and the probabilistic damage identification method. In this method, the influence of the damage wave packet migration on the correlation coefficient between the reconstructed signals of each sensing path and the initial excitation signal is analyzed, and the structure is divided into multiple regional units corresponding to the damage to locate damage. In addition, the influence of the number of sensing paths on the location accuracy is also analyzed. A method of damage probability imaging based on structural symmetry is proposed to enhance location accuracy in the case of sparse sensing paths. The experimental and simulation results verify that the method can achieve damage location with fewer excitation times. Moreover, this method can avoid the problem that the damage wave packet is difficult to extract, improve the efficiency of damage location, and promote the engineering application of the Lamb wave damage location method. [ABSTRACT FROM AUTHOR]

Motivated by recent observations of rapid (interannual) signals in the geomagnetic data, and by advances in numerical simulations approaching the Earth's outer core conditions, we present a study on the dynamics of hydromagnetic waves evolving over a static base state. Under the assumption of timescales separation between the rapid waves and the slow convection, we linearize the classical magneto-hydrodynamics equations over a steady non-axisymmetric background magnetic field and a zero velocity field. The initial perturbation is a super-rotating pulse of the inner core, which sets the amplitude and length scales of the waves in the system. The initial pulse triggers axisymmetric, outward propagating torsional Alfvén waves, with characteristic thickness scaling with the magnetic Ekman number as EkM1/4. Because the background state is non-axisymmetric, the pulse also triggers non-axisymmetric, quasi-geostrophic (QG) Alfvén waves. As these latter waves propagate outwards, they turn into QG, magneto-Coriolis (QG-MC) waves as the Coriolis force supersedes inertia in the force balance. The period of the initial wave packet is preserved across the shell but the QG-MC wavefront disperses and a westward drift is observed after this transformation. Upon reaching the core surface, the westward drift of the QG-MC waves presents an estimated phase speed of about 1100kmy−1. This analysis confirms the QG-MC nature of the rapid magnetic signals observed in geomagnetic field models near the Equator. [ABSTRACT FROM AUTHOR]

Vortex light, characterized by an intrinsic orbital angular momentum aligned with its propagation direction, is described through vortex electromagnetic waves. Similar to the gravitational spin Hall effect (SHE), vortex light is expected to exhibit intrinsic orbital angular momentum dependent trajectories and deviations from the null geodesic plane when propagating through a gravitational field, a phenomenon termed the gravitational orbital Hall effect (OHE). In this work, we model the vortex light as vortex Laguerre–Gaussian electromagnetic wave packets and analyze its motion by solving covariant Maxwell equations within the Lense–Thirring metric. Our findings reveal that the trajectory of vortex light with an intrinsic orbital angular momentum deviates from the null geodesic in two ways. It deviates both perpendicular to, and within, the null geodesic plane. This behavior contrasts with the gravitational SHE, where spin-polarized light primarily deviates perpendicular to the null geodesic plane. Moreover, the relationship between the deviation and intrinsic orbital angular momentum differs significantly from that between the deviation and spin. These results suggest a unique interaction between intrinsic orbital angular momentum and gravity, distinct from the spin-gravity coupling, indicating that the gravitational OHE of light might not be precisely predicted by merely substituting spin with intrinsic orbital angular momentum in the gravitational SHE of light. [ABSTRACT FROM AUTHOR]

We study semiclassical perturbations of single-degree-of-freedom Hamiltonian systems possessing hyperbolic saddles with homoclinic orbits, and provide a sufficient condition for the separatrices to split, using a Melnikov-type approach. The semiclassical systems give approximations of the expectation values of the positions and momenta to the semiclassical Schrödinger equations with Gaussian wave packets as the initial conditions. The occurrence of separatrix splitting explains a mechanism for the existence of trajectories to cross the separatrices on the classical phase plane in the expectation value dynamics. Such separatrix splitting does not occur in standard systems of Hagedorn and Heller for the semiclassical Gaussian wave packet dynamics as well as in the classical systems. We illustrate our theory for the potential of a simple pendulum and give numerical computations for the stable and unstable manifolds in the semiclassical system as well as solutions crossing the separatrices. [ABSTRACT FROM AUTHOR]

Continuing from Paper I [Ohsawa and Yagasaki, J. Math. Phys. 65, 102706 (2024)], we study semiclassical perturbations of single-degree-of-freedom analytic Hamiltonian systems and provide a sufficient condition for its meromorphic nonintegrability such that the first integrals depend on the small parameter meromorphically. Our approach is based on a generalization due to Ayoul and Zung of the Morales-Ramis theory, which enables us to show the meromorphic nonintegrability of dynamical systems by using the differential Galois theory. We remark that standard systems of Hagedorn and Heller for the semiclassical Gaussian wave packet dynamics are analytically integrable as well as the corresponding classical systems. We illustrate our theory for a bounded potential. [ABSTRACT FROM AUTHOR]

For many nonlinear applications described by the dynamics of nonlinear Schrödinger equation with higher-order terms (HONLSE) such as nonlinear optics, space plasma physics molecular biology, astrophysics, quantum mechanics, superfluid, fluid mechanics, and fiber optics communications, a unique closed-form solution have been obtained using energy equation. In addition, some new solitary solutions HONLSE have been obtained via the unified solver method. The resultant solutions behave as breathers, super solitons, envelope breathers, blow up, localized super waves, periodical super shock, train super solitons, and shock structures. The modulations of Kerr nonlinear, chromatic dispersive, and wave packet drift parameters on the wave characteristics of the obtained solutions have been investigated. It was reported that the model parameters affect the amplitude, steepness, and width of the resultant structures. The provided solution can be used as a box solver for a variety of natural science systems described by distinct nonlinear equations. [ABSTRACT FROM AUTHOR]

In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and coupled wave packets in nonlinear optical fibers and describes transverse effects in nonlinear fiber optics. Initially, a complex transformation is used to convert the model into a single Nonlinear Ordinary Differential Equation (NODE), from which hyperbolic, exponential, rational, trigonometric, and rational hyperbolic solutions are produced. In order to better understand the physical dynamics, we offer several 3D, contour, and 2D illustrations for the independent selections of physical parameter values. These illustrations highlight the graphic behaviour of some optical solitons and demonstrate that, under certain constraint conditions, acquired optical solitons lose their stability when they approach an axis and display periodic-axial perturbations, which lead to the generation of optical fractals. As a framework, the generated optical solitons have several useful applications in the field of telecommunications. Furthermore, our suggested RMESEM demonstrates its use by broadening the spectrum of optical soliton solutions, offering important insights into the dynamics of the CNHEs, and suggesting possible applications in the management of nonlinear models. [ABSTRACT FROM AUTHOR]

The propagation of a wave packet in a discontinuous medium, one of them with absorption of energy, has been studied analytically. We examined an electromagnetic pulse starting in a free medium and moving toward a dissipative one. In the first medium, the wave is free-moving governed by the wave equation, while in the second medium, the wave is affected by the Joule effect governed by the telegrapher's equation. We solved the motion at the discontinuity using the Fourier representation for a wave packet in the formalism of a wave attenuated approach. This allowed us to calculate a reflection amplitude in analogy with the ordinary definition at a discontinuity in a medium without dissipation but with different velocities in each medium. [ABSTRACT FROM AUTHOR]

We consider semiclassically scaled, weakly nonlinear Schrödinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross–Pitaevskii theory of trapped, rotating quantum gases. We construct asymptotic solutions in the form of semiclassical wave packets, which are concentrated in both space and in frequency around an classical Hamiltonian phase-space flow. The rotation term is thereby seen to alter this flow, but not the corresponding classical action. [ABSTRACT FROM AUTHOR]

Classical curl forces are position-dependent Newtonian forces (accelerations) that are not the gradient of a scalar potential, and in general cannot be described by Hamiltonians. However, a special class of curl forces can be described by Hamiltonians, with the unusual feature that the kinetic energy is anisotropic in the momentum components. Therefore they can be quantised conventionally. We quantise the simplest such case: motion in the plane, with a curl force azimuthally directed and linear. As expected, the quantum propagator, and the way this drives Gaussian wavepackets, directly reflects the spiralling classical curl force dynamics. Two classes of stationary states—eigenfunctions of a continuous spectrum for the unbounded Hamiltonian—are described. They possess unusual singularities and an unfamiliar quantisation condition; their explanation requires asymptotics and unfamiliar singularities in the underlying families of classical trajectories. The analysis is supported and illustrated numerically. [ABSTRACT FROM AUTHOR]

In this study, we investigate the transport properties of Airy and Hermit-Gaussian wavepackets traveling through a Gaussian potential well in the standard and fractional media. We use a split step Fourier method to solve the corresponding two-dimensional fractional nonlinear linear Schrodinger equation. We study the interference phenomenon, Huygens principle and trapping properties of the system in different situations. For this purpose, the position of the system has also selected inside the potential well to consider the wavepacket evolution. Then, the effect of the well and incident wavepackets parameters on the evolution the transport properties of employed wavepackets have properly been considered. [ABSTRACT FROM AUTHOR]