Wave Packet Propagation Research Articles

Multi‐Ion Oscillitons—Origin of Coherent Magnetospheric EMIC Waves

AbstractThe recent spacecraft observations by MMS and Van Allen Probes associated with electromagnetic ion cyclotron (EMIC) waves in the Earth magnetosphere emphasize the important role of multi‐ion plasma composition for generation and characteristics of these emissions. We show that main properties of the coherent EMIC waves can be explained with the concept of “multi‐ion oscillitons” (Sauer et al., 2001, https://doi.org/10.1029/2001GL013047). In a plasma with two types of ions of different masses (e.g., protons and oxygen ions), oscillitons arise from the exchange of momentum and energy between the two ion components, with the electromagnetic field acting as a mediator. At frequencies near cross‐over frequencies of different wave modes in the multi‐ion plasma the nonlinear resonance which strongly amplifies the seed unstable mode can be excited. A small phase difference in oscillations of different ion species leads to a nonlinear wave beating and generation of wave packets. The “resonance” frequency is characterized by a local maximum of the phase velocity and the coincidence of phase and group velocity. It is suggested that the oscillitons are triggered by the instability due to the proton temperature anisotropy and may survive outside the source region for long distances. The generation of coherent waves by oscillitons is of a general nature and may contribute to understand the manifold of phenomena in other space plasma environments in which the dynamics of minor ion admixtures cannot be neglected. The concept of oscillitons can also be applied to the momentum exchange between particle groups of the same mass, but different temperature.

Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice

To simulate the dynamics of massless Dirac fermions in curved space-times with one, two, and three spatial dimensions, we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved space-time. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasiconservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.

Nonadiabatic Vibrational Resonance Raman Spectra from Quantum Dynamics Propagations with LVC Models. Application to Thymine.

We present a viable protocol to compute vibrational resonance Raman (vRR) spectra for systems with several close-lying and potentially coupled electronic states. It is based on the parametrization of linear vibronic coupling (LVC) models from time-dependent density functional theory (TD-DFT) calculations and quantum dynamics propagations of vibronic wavepackets with the multilayer version of the multiconfiguration time-dependent Hartree (ML-MCTDH) method. Our approach is applied to thymine considering seven coupled electronic states, comprising the three lowest bright states, and all vibrational coordinates. Computed vRR at different excitation wavelengths are in good agreement with the available experimental data. Up to 250 nm the signal is dominated by the lowest HOMO → LUMO transition, whereas at 233 nm, in the valley between the two lowest energy absorption bands, the contributions of all the three bright states, and their interferences and couplings, are important. Inclusion of solvent (water) effects improves the agreement with experiment, reproducing the coalescence of vibrational bands due to CC and C=O stretchings. With our approach we disentangle and assess the effect of interferences between the contribution of different quasi-resonant states to the transition polarizability and the effect of interstate couplings. Our findings strongly suggest that in cases of close-lying and potentially coupled states a simple inclusion of interference effects is not sufficient, and a fully nonadiabatic computation should instead be performed. We also document that for systems with strong couplings and quasi-degenerate states, the use of HT perturbative approach, not designed for these cases, may lead to large artifacts.

Multilayer Multiconfiguration Time-Dependent Hartree Study on the Mode-/Bond-Specific Quantum Dynamics of Water Dissociation on Cu(111).

In this work, full-dimensional (9D) quantum dynamics calculations on mode-/bond-specific surface scattering of a water molecule on a copper (111) rigid surface are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. To easily perform the ML-MCTDH calculations on such a triatomic molecule-surface system, we first choose specific Jacobi coordinates as a set of coordinates of water. Next, to efficiently perform the 9D ML-MCTDH wavepacket propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific dissociation probabilities of H2O on Cu(111) are computed, and mode-/bond-specific dynamics are demonstrated by comparison with a probability curve computed for a water molecule in the ground state. The dependence of the dissociation probability of the initial state of H2O is studied, and it is found that the excitation-specific dissociation probabilities can be divided into three groups. We find that the vibrationally excited states enhance the dissociation reactivity of H2O, while the rotationally excited states hardly influence it.

Persistent homology analysis of a generalized Aubry-André-Harper model

Observing critical phases in lattice models is challenging due to the need to analyze the finite time or size scaling of observables. We study how the computational topology technique of persistent homology can be used to characterize phases of a generalized Aubry-Andr\'e-Harper model. The persistent entropy and mean squared lifetime of features obtained using persistent homology behave similarly to conventional measures (Shannon entropy and inverse participation ratio) and can distinguish localized, extended, and critical phases. However, we find that the persistent entropy also clearly distinguishes ordered from disordered regimes of the model. The persistent homology approach can be applied to both the energy eigenstates and the wave packet propagation dynamics.

Wave Packet Calculation of Absolute UV Cross Section of Criegee Intermediates.

Criegee intermediates, R1R2COO, are reactive species formed in the atmosphere through the ozonolysis of alkenes. They have an intense ultraviolet (UV) adsorption between 300 to 400 nm. However, experimentally determining the absolute cross sections is not easy. We used wave packet propagation on an one-dimensional adiabatic potential energy curve (PEC) along the OO bond to simulate the UV spectra for various Criegee intermediates. Our results showed a very fast, ∼20 fs, decay out of the Franck-Condon region. This gives justification for using the semiclassical approach which was utilized in previous studies. From the comparison of various quantum chemistry methods, we found that multireference methods can give spectra with a width and cross section reproducing the experimental results, while single reference methods tend to give narrower skewed peaks with a larger cross section. From the test using wave packet propagation on various approximated PECs and transition moment functions, we show that the Gaussian approximation within the reflection method is valid. In addition, we found that we can obtain peak positions that reproduce the experimental results by shifting those obtained by MRCI+Q, CASSCF, EOMCCSD, and TDCAMB3LYP by -0.2, -1.0, -0.3, and -0.5 eV, respectively. The Gaussian approximation using peak position, oscillator strength, and peak width from MRCI+Q is a cost-effective way to simulate the UV spectra of Crigee intermediates for which experimental determination may be hard.

Local effects during ion scattering on adsorbate-covered surfaces

This study addresses the importance of adsorbate-induced local effects during collisions between projectiles and adsorbate-covered surfaces. Various systems are investigated: H− on Na/Ag(111); H− on Na/Cu(111); and Li+ on K/Al(100), by using wave packet propagation methods. From the projectile's perspective, the adsorbate's presence on the surface can be felt from up to a few tens of atomic units away when the projectile is close to the surface, and up to 100 a.u or more when the projectile is on top of adsorbate. This is a well-defined bell-shape region around the adsorbate. However, the scattered ion/neutral fractions are not significantly affected unless the projectile impacts the surface in the close 10–15 a.u. vicinity of the adsorbate. Scattering from adsorbate sites compared to scattering from substrate sites produces very different ion/neutral fractions, that vary not only with the surface coverage, but especially with the distance from the projectile's point of impact on the surface to the adsorbate. Our calculated Li neutral fractions obtained after scattering Li+ from K/Al(100) are in satisfactory agreement with the experimental results.

Analysis of single-photon self-interference in Young’s double-slit experiments

For centuries Young’s double-slit interference continues to be a hot discussion subject about whether light is waves or particles. This work unravels the self-interference parados, and sheds light on such a concept that assumes a photon can split, self-interfere, and recombine. This work elucidates how coherent photons from a laser source could produce a double-slit interference pattern without the hypothesis of unphysical splitting and recombination of a single photon. Unlike the conventional single wave-function description for the whole ensemble of particles, we develop a pilot-wave trajectory approach to track every photon’s wave-packet propagation and calculate the evolution of the interference intensity in time. We demonstrate how wave packets and phase coherence affect the interference pattern. To resolve the century-old self-interference paradox, we show that such an hypothesis is unnecessary, and the illusion is due to the long coherence length of laser photons and overlaps of delocalized light wave packets.

Nondispersive Space–Time Wave Packets Propagating in Dispersive Media

AbstractSpace–time wave packets can propagate invariantly in free space with arbitrary group velocity thanks to the spatio‐temporal correlation. Here it is proved that the space–time wave packets are stable in dispersive media as well and free from the spread in time caused by material dispersion. Furthermore, the law of anomalous refraction for space–time wave packets is generalized to the weakly dispersive situation. These results reveal new potential of space–time wave packets for the applications in real dispersive media.

Distinctive onset of electron correlation in molecular tautomers

We investigate the attosecond response of the electronic cloud of a molecular system to an outer-valence ionization. The time needed for the remaining electrons to respond to a sudden perturbation in the electronic structure of the molecule is a measure of the degree of electron correlation. Using the ab initio multielectron wave-packet propagation method, we show that this response time can be sensitive to the molecular structure and the symmetry of the ionized molecular orbital. Our analysis revealed differences in the temporal signatures of ultrafast charge migration processes in the context of tautomeric hydrogen in multinuclear systems, and the relevance of distinctive onset of electron correlation within the overall molecular complexity.

Atomistic evidence of hydrodynamic heat transfer in nanowires

With wave-packet propagation simulations and heat flux estimation via molecular dynamics, we show that the heat flux radial distribution in silicon nanowires can be described by a mesoscopic model, the hydrodynamic heat equation. We observe Poiseuille like heat flux profile, that cannot be described by a simple kinetic model such as the Fuchs-Sondheimer model, in both pristine and core/shell nanowires. The addition of a shell does not change the shape of the radial heat flux distribution, but just modifies the maximum of the heat flux in the center of the nanowire. These results show that there is a heat flux depletion length for pristine or core shell nanowires, 1–2 nm away from the boundary of the crystalline part. The parameters of the mesoscopic model are discussed in terms of microscopic properties, including the phonon mean free path as function of frequency and the partial vibrational density of states in the different regions of the nanowire.

Semiclassical propagation of coherent states and wave packets: Hidden saddles.

Semiclassical methods are extremely important in the subjects of wave-packet and coherent-state dynamics. Unfortunately, these essentially saddle-point approximations are considered nearly impossible to carry out in detail for systems with multiple degrees of freedom due to the difficulties of solving the resulting two-point boundary-value problems. However, recent developments have extended the applicability to a broader range of systems and circumstances. The most important advances are first to generate a set of real reference trajectories using appropriately reduced dimensional spaces of initial conditions, and second to feed that set into a Newton-Raphson search scheme to locate the exposed complex saddle trajectories. The arguments for this approach were based mostly on intuition and numerical verification. In this paper, the methods are put on a firmer theoretical foundation and then extended to incorporate saddles hidden from Newton-Raphson searches initiated with real trajectories. This hidden class of saddles is relevant to tunneling-type processes, but a hidden saddle can sometimes contribute just as much as or more than an exposed one. The distinctions between hidden and exposed saddles clarifies the interpretation of what constitutes tunneling for wave packets and coherent states in the time domain.

On the Role of Molecular Polarizability in Positron Coupling to Vibrations in Homonuclear Diatomics

In a previous work [Poveda, Varella, and Mohallem (Poveda et al., Atoms, 2021, 9: 64) it was shown that the bell-like shape of the 0 → 1 vibrational excitation cross section of H2 as a function of the incoming positron energy, with its characteristic sharp onset at threshold, can be accounted for by a simple model which couples the positron to the vibrational mode of the molecule, throught the behavior of the target polarizabitity with the internuclear bond distance. The study, carried out via time-dependent wave-packet dynamics propagation, relies on a two-dimensional potential energy surface involving just the scattering (positron-target) and vibrational (target) coordinates. Here the model is extended to the full three-dimensional configuration space of the positron-diatomic complex, with the cross sections computed within a time-independent close-coupling approach. The present results confirm the previous findings, shedding light on the mechanisms through which a low-energy positron couples to the molecular vibrations.

Backward- and forward-wave soliton coexistence due to second-neighbor coupling in a left-handed transmission line

We study analytically and numerically the impact of the second-neighbor interactions on the propagation of an initial wave-packet through a coupled nonlinear left-handed transmission line. We start with a detailed analysis of the dispersion curve and group velocity. We then use the quasi-discrete approximation with respect to long wavelength transverse perturbations to reduce the nonlinear discrete model of the lattice to a nonlinear Schrödinger equation. A detailed analysis of the product of the group velocity dispersion (P) and the nonlinear term (Q) is presented with respect to the relevant parameters of the system. Here we see the important role of the second-neighbor coupling, which makes the dispersion curve non-monotonic. Thus, for a given frequency, the group velocity can be both positive and negative, while for each choice the product, PQ, can be either positive or negative. Our numerical results confirm that for sufficiently strong second-neighbor coupling, bright backward-wave pulses and dark solitons can coexist at a common frequency, and these travel in opposite directions through the lattice.

Circumglobal Rossby wave patterns during boreal winter highlighted by space–time spectral analysis

Abstract. The classic partitioning between slow-moving, low-wavenumber planetary waves and fast-moving, high-wavenumber synoptic waves is systematically extended by means of a space–time spectral decomposition to characterize the day-to-day evolution of Rossby wave activity in the upper troposphere. This technique is employed to study the origin and the propagation of circumglobal Rossby wave patterns (CRWPs), amplified Rossby waves stretching across the Northern Hemisphere in the zonal direction and projecting primarily over few, dominant wavenumber–phase-speed harmonics. Principal component analysis of daily anomalies in spectral power allows for two CRWPs to emerge as leading variability modes in the spectral domain during boreal winter. These modes correspond to the baroclinic propagation of Rossby wave packets (RWPs) from the Pacific to the Atlantic storm track in a hemispheric flow configuration displaying enhanced meridional gradients of geopotential height over midlatitudes. The first CRWP is forced by tropical convection anomalies over the Indian Ocean and features the propagation of amplified RWPs over northern midlatitudes, while the second one propagates rapidly over latitudes between 35 and 55∘ N and appears to have extratropical origin. An anomalous equatorward propagation of Rossby waves from the Atlantic eddy-driven jet to the North African subtropical jet is observed for both CRWPs. The obtained results highlight the substantial contribution of propagating RWPs to CRWPs, hinting that the two features might have the same nature.

Optical properties of para‐oligophenylenes: A case study of electronic absorption spectrum and relaxation dynamics of terphenyl

AbstractWe present a detailed quantitative description of vibronic‐coupling effects on the singlet photophysics of para‐oligophenylenes. Four energetically close‐lying singlet states (S1, S2, S3, and S4) are taken into consideration to interpret the first UV/Vis absorption band of these molecules. As a representative example, the energetics of those four states are evaluated for para‐terphenyl by performing extensive electronic structure calculations within the linear vibronic coupling framework. We obtain absorption spectral profiles by wavepacket propagation technique using the multi‐configuration time‐dependent Hartree method. Computed spectral profiles are in accord with the experiment. A minor electronic population transfer to upper states on a timescale of 10 fs is observed, suggesting the excited‐state nonadiabatic behavior of the molecule. Our findings necessitate the experimental validation of the role of higher states in the spectroscopy and dynamics of photoexcited para‐oligophenylenes.

Trajectories and the perception of classical motion in the free propagation of wave packets

AbstractThe free propagation in time of a normalisable wave packet is the oldest problem of continuum quantum mechanics. Its motion from microscopic to macroscopic distance is the way in which most quantum systems are detected experimentally. Although much studied and analysed since 1927 and presented in many textbooks, here the problem is re‐appraised from the standpoint of semi‐classical mechanics. Particular aspects are the emergence of deterministic trajectories of particles emanating from a region of atomic dimension and the interpretation of the wave function as describing a single particle or an ensemble of identical particles. Of possible wave packets, that of Gaussian form is most studied due to the simple exact form of the time‐dependent solution in real and in momentum space. Furthermore, this form is important in laser optics. Here the equivalence of the time‐dependent Schrödinger equation to the paraxial equation for the propagation of light is demonstrated explicitly. This parallel helps to understand the relevance of trajectory concepts and the conditions necessary for the perception of quantum motion as classical.Key Points The paper addresses a problem of fundamental quantum mechanics, important in both physics and chemistry. Within physics, the subject is relevant to the disciplines of both quantum mechanics and classical optics. The matter presented is topical also for researchers in the history and philosophy of physics.

Simulations of molecular photodynamics in long timescales.

Nonadiabatic dynamics simulations in the long timescale (much longer than 10 ps) are the next challenge in computational photochemistry. This paper delimits the scope of what we expect from methods to run such simulations: they should work in full nuclear dimensionality, be general enough to tackle any type of molecule and not require unrealistic computational resources. We examine the main methodological challenges we should venture to advance the field, including the computational costs of the electronic structure calculations, stability of the integration methods, accuracy of the nonadiabatic dynamics algorithms and software optimization. Based on simulations designed to shed light on each of these issues, we show how machine learning may be a crucial element for long time-scale dynamics, either as a surrogate for electronic structure calculations or aiding the parameterization of model Hamiltonians. We show that conventional methods for integrating classical equations should be adequate to extended simulations up to 1 ns and that surface hopping agrees semiquantitatively with wave packet propagation in the weak-coupling regime. We also describe our optimization of the Newton-X program to reduce computational overheads in data processing and storage.This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.

Continuum Electronic States: The Tiresia Code.

A multicenter (LCAO) B-spline basis is described in detail, and its capabilities concerning affording convergent solutions for electronic continuum states and wavepacket propagation are presented. It forms the core of the Tiresia code, which implements static-DFT and TDDFT hamiltonians, as well as single channel Dyson-DFT and Dyson-TDDFT descriptions to include correlation in the bound states. Together they afford accurate and computationally efficient descriptions of photoionization properties of complex systems, both in the single photon and strong field environments. A number of examples are provided.

Effective Phase Space Representation of the Quantum Dynamics of Vibrational Predissociation of the ArBr2(B,ν =16···25) Complex.

We perform trajectory-based simulations of the vibrational predissociation of the ArBr2(B,ν=16···25) van der Waals triatomic complex, constrained to the T-shape geometry. To this aim, we employ a 2-fold mapping of the quantum dynamics into classical-like dynamics in an extended phase space. The effective phase space comprises two distinct sets of degrees of freedom, namely a collection of coupled harmonic oscillators and an ensemble of quantum trajectories. The time evolution of these variables represent bound and unbound motions of the quantum system, respectively. Quantum trajectories are propagated within the interacting trajectory representation. The comparison between the lifetimes of the predissociating complexes computed using the trajectory-based approach and the experimental results available for the target systems indicates that the present method is competitive with wavepacket propagation techniques. The competition between several simultaneous vibrational relaxation pathways was found to have a direct impact on the time scales of vibrational predissociation. Likewise, the analysis of the time evolution of the trajectories reveals the existence of regions in the effective phase space where transitions to vibrational states of higher energy are more likely to occur. The size and location of these regions influence the transient vibrational distributions and therefore the computed lifetimes. Furthermore, the mechanisms of energy redistribution along the dissociation coordinate are analyzed.