Wave Packet Propagation Research Articles

Accelerating wavepacket propagation with machine learning.

In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time-dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed-up from the FNO method allows for its combination with the Markov-chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes.

Dynamic protected states in the non-Hermitian system

The non-Hermitian skin effect and nonreciprocal behavior are sensitive to the boundary conditions, which are unique features of non-Hermitian systems. In such systems, eigenenergies can become complex, and all eigenstates tend to localize at the boundary, a phenomenon that contrasts with Hermitian topologies. In this work, we theoretically study the dynamic behavior of the propagation of Gaussian wavepackets inside a non-Hermitian lattice and analyze the self-acceleration process of bulk state or Gaussian wavepackets toward the system’s boundary. The initial wavepackets will not only propagate toward the side where the eigenstates are localized, but also their momentum will approach to a specific value. This value corresponds to the maximum imaginary components of the energy dispersion. In addition, if the wavepackets in the momentum space cover this specific momentum, they will eventually exhibit exponentially increasing amplitudes with time evolution, maintaining the dynamic protected condition for an extended period of time until they approach the boundary. We also take two widely used toy models as examples in one and two dimensions to verify the correspondence of the non-Hermitian skin effect and the dynamic protected state.

Probing general relativistic spin–orbit coupling with gravitational waves from hierarchical triple systems

ABSTRACT 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.

Enhanced damping and bandwidth in roton-like dispersion of a beyond nearest neighbor periodic chain

This paper investigates the intriguing roton-like phenomenon occurring in systems with non-local interactions, wherein a single dispersion curve exhibits positive and negative group velocities. Previous research has predominantly concentrated on investigating the roton dispersion in undamped metamaterials through steady-state vibration and driven wave methodologies. However, exploring transient wave propagation in damped metamaterials, employing a free wave approach to study damping enhancement (metadamping), has received comparatively little attention. Addressing this research gap, the damping of the system is quantified as the rate of decay of transient vibrations. Results show a significant increase in damping and attenuation bandwidth, coinciding with the presence of the roton-like phenomenon. Unlike previous studies on metadamping, the proposed beyond nearest neighbor (BNN) chain simultaneously enhances both damping and reduction in acoustic bandwidth without sacrificing either property. Spatiotemporal domain simulation evidenced the existence of backward propagating wave packets due to a roton-like phenomenon in the specific frequency range.

Different kinds of accelerated propagation of relativistic electromagnetic plasma wavepackets

Relativistic electromagnetic plasma waves are described by a dynamical equation that can be solved not only in terms of plane waves, but also for several different accelerating wavepacket solutions. Depending on the spatial and temporal dependence of the plasma frequency, different kinds of accelerating solutions can be obtained, for example, in terms of Airy or Weber functions. Also, we show that an arbitrary accelerated wavepacket solution is possible, for example, for a system with a luminal plasma slab.

Quantum dynamical study on 15N ＋ 14N14N isotope exchange reactions at high energies

In this study, we conduct quantum dynamical calculations at relatively high energies on the exchange reaction 15N ＋ 14N14N →15N14N ＋ 14N on its ground electronic N3 (4A′′) potential energy surface (PES) utilizing the time-dependent wave packet (TDWP) propagation method. Our primary focus is on analyzing the reaction mechanism for 15N ＋ ortho-14N14N (j = 0) and para-14N14N (j = 1) cases. We also explore the influence of varying J (up to 120) of the three-body system and the initial vibrational level (ν = 1, 5, 10) of the diatom on the reaction probability (RP) for ortho and para configurations.

Studying the effect of delamination on Ostrovsky wave packet propagation in waveguides

Studying the effect of delamination on Ostrovsky wave packet propagation in waveguides

Envelope solitary waves in two-negative ions with stationary dust grains

Using a multi-fluid model, we look at how modulated electrostatic dust-ion-acoustic wave packets move nonlinearly through a plasma made up of a three-ion fluid with Maxwellian electrons and stationary dust grains. A nonlinear Schrödinger (NLS) equation describes the electric potential envelope wave packet. The analysis reveals the existence of different types of localized modes, namely bright, dark, and grey solitons. We numerically analyse the coefficients of the NLS equation to identify stable or unstable regions for wave packet propagation. It is found that higher relative density ratios increase the group velocity of the wave packets. Stable pulses can become unstable when plasma parameters exceed certain relative density ratio values. Stable pulses can exist within a crucial window of the relative dust density ratio. Controlling the dust grain density ratio outside the zone can cause unstable wave packets or bright envelope solitons to propagate.

Parametric Decay of a Kinked Alfvén Wave Packet: 3D Magnetohydrodynamic Simulations

Large amplitude Alfvénic fluctuations, sometimes leading to localized inversions of the magnetic field, called switchbacks, are a common but poorly understood phenomenon in the solar wind. In particular, their origin(s), evolution, and stability within solar wind conditions are yet to be fully understood. Simulations modeling switchbacks have previously studied their stability in 2D. Here, we investigate the decay process of Alfvén wave packets via MHD simulations in 3D by characterizing the effects of system size, aspect ratio, and propagation angle on the decay rate. We show that the initial wave packet is unstable to parametric instabilities that develop compressible and Alfvénic secondary modes in the plane of, and transverse to, the initial wave packet propagation direction. The growth of transverse modes, absent in 2D simulations, increases the decay rate of the wave packet. We finally discuss the implications of our results for lifetime estimates of switchbacks and wave energy conversion in the solar wind.

Multi-state vibronic dynamics of the benzene cation: Combined multi-mode Jahn-Teller and Pseudo Jahn-Teller Effects

The multi-state vibronic interactions in the benzene radical cation are investigated theoretically, based on an ab initio quantum dynamical approach. The three lowest doubly degenerate and two lowest non-degenerate electronic states are included, amounting to eight electronic component states and 28 vibrational degrees of freedom. The multi-mode dynamical Jahn-Teller as well as pseudo Jahn-Teller effects are included on an equal footing. This becomes possible by employing the Multiconfigurational Time-Dependent Hartree Method and its multi-layer extension for the wavepacket propagation underlying the dynamical treatment. The results indicate a step wise population transfer from higher to lower-energy electronic states. The transfer between the highest ( E∼ and D∼ states) is extremely fast which is made plausible by their energetic proximity. On the other hand the transfer is not complete and does not comprise the X∼ ground state. Rather, a substantial part of the population gets trapped in the lowest excited ( B∼ ) state. The phenomenon is briefly discussed and calls for future work on this intricate dynamical system.

Linear Vibronic Coupling Approach for Surface-Enhanced Raman Scattering: Quantifying the Charge-Transfer Enhancement Mechanism.

The outstanding amplification observed in surface-enhanced Raman scattering (SERS) is due to several enhancement mechanisms, and standing out among them are the plasmonic (PL) and charge-transfer (CT) mechanisms. The theoretical estimation of the enhancement factors of the CT mechanism is challenging because the excited-state coupling between bright plasmons and dark CT states must be properly introduced into the model to obtain reliable intensities. In this work, we aim at simulating electrochemical SERS spectra, considering models of pyridine on silver clusters subjected to an external electric field E⃗ that represents the effect of an electrode potential Vel. The method adopts quantum dynamical propagations of nuclear wavepackets on the coupled PL and CT states described with linear vibronic coupling models parametrized for each E⃗ through a fragment-based maximum-overlap diabatization. By presenting results at different values of E⃗, we show that indeed there is a relation between the population transferred to the CT states and the total scattered intensity. The tuning and detuning processes of the CT states with the bright PLs as a function of the electric field are in good agreement with those observed in experiments. Finally, our estimations for the CT enhancement factors predict values in the order of 105 to 106, meaning that when the CT and PL states are both in resonance with the excitation wavelength, the CT and PL enhancements are comparable, and vibrational bands whose intensity is amplified by different mechanisms can be observed together, in agreement with what was measured by typical experiments on silver electrodes.

Ultrafast Excited-State Nonadiabatic Dynamics in Pt(II) Donor-Bridge-Acceptor Assemblies: A Quantum Approach for Optical Control.

The ultrafast nonadiabatic excited state dynamics of (PTZ-N-benzyl-acetylide) (trans-bis-trimethylphosphine) Pt(II) (acetylide-NDI-bis-methyl) 1, representative of a series of Pt(II) donor-bridge-acceptor assemblies experimentally studied by the Weinstein group, University of Sheffield, is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. On the basis of electronic structure data obtained at the time-dependent density functional theory (TD-DFT) level, the subpicosecond decay is simulated by solving an 11 electronic states multimode problem, up to 18 vibrational normal modes, including both spin-orbit coupling (SOC) and vibronic coupling. A careful analysis of the results, within the diabatic representation, provides the key features of the spin-vibronic mechanism at work in this complex, distinguishing between the spin-orbit and vibronically activated ultrafast processes within the excited states manifold. The knowledge of the key active normal modes that promote selectively the population of specific electronic excited states opens a route toward optical control by selectively exciting these modes in order to drive the associated nonadiabatic processes. Relevant simulations, over 2 ps, are proposed to assess the impact of these selective vibrational excitations on the branching ratio between the primary photoproducts, namely, bridge-acceptor charge-transfer (CT) and donor-acceptor charge-separated (CS) electronic states. Whereas the excitation of the localized acetylide bridge C≡C bond stretching does not modify drastically the population of the low-lying electronic states within the first two ps, vibrational excitation of the out-of-plane twisting motion of the N-benzyl group linked to the donor entity favors the population of the 1,3CS states at the expense of the lowest 1,3CT states. This quantum study opens the route to IR optical control experiments based on the specific alteration of vibrational normal modes that activate vibronic couplings between key electronic excited states. However, the presence of critical crossings along the PES channels associated with these normal modes and the role of concurrent SOC driven ultrafast transfers of population should not be underestimated.

Vibronic coupling and ultrafast relaxation dynamics in the first five excited singlet electronic states of bithiophene.

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 abinitio 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 ∼100fs. Totally symmetric C=C stretching, C-S stretching, C-H wagging, ring puckering, and inter-ring bending modes collectively drive such relaxation dynamics.

Phonon-Driven Femtosecond Dynamics of Excitons in Crystalline Pentacene from First Principles.

Nonradiative exciton relaxation processes are critical for energy transduction and transport in optoelectronic materials, but how these processes are connected to the underlying crystal structure and the associated electron, exciton, and phonon band structures, as well as the interactions of all these particles, is challenging to understand. Here, we present a first-principles study of exciton-phonon relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyze key scattering channels. We find that both exciton intraband scattering and interband scattering to parity-forbidden dark states occur on the same ∼100 fs timescale as a direct consequence of the longitudinal-transverse splitting of the bright exciton band. Consequently, exciton-phonon scattering exists as a dominant nonradiative relaxation channel in pentacene. We further show how the propagation of an exciton wave packet is connected with crystal anisotropy, which gives rise to the longitudinal-transverse exciton splitting and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding the role of exciton-phonon interactions in exciton nonradiative lifetimes in molecular crystals and beyond.

Designer quantum reflection from a micropore

We expand the theoretical toolbox for controllable quantum reflection by departing from a simple planar reflector. We introduce a circular hole (a micropore) of variable size, for which the electrostatic image potential can be exactly calculated. We combine this with two-dimensional simulations of wave-packet propagation at arbitrary angles of incidence to show that the quantum reflection probability can be tuned over a wide range of values. Published by the American Physical Society 2024

Excitation energy transfer and vibronic relaxation through light-harvesting dendrimer building blocks: A nonadiabatic perspective.

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like π-conjugated macromolecules) involve a directional cascade of local excitation energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally excited electronic states via conical intersections. The smallest PPE building block that is able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (hence, 2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From linear-response time-dependent density functional theory electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1 + 2)-state-8-dimensional vibronic-coupling Hamiltonian model for running subsequent multiconfiguration time-dependent Hartree wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted herein through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity.

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

To better understand the mechanisms underlying the formation of blocking highs over the North Atlantic as a type of large-amplitude disturbance, this paper reports results from numerical experiments within the framework of local finite-amplitude wave activity (LWA). The numerical model employed in this study explicitly depicts two important atmospheric internal dynamic processes—nonlinear zonal eddy flux and Rossby wave packet propagation—which have been individually emphasized by different previous studies. The simulation results reveal that these two dynamic processes are the dominant contributors to the formation of Atlantic blocking cases. However, they exert different influences over different regions. The southern and northern parts of the primary LWA associated with the blocking cases are mainly induced by the nonlinear zonal eddy flux and Rossby wave packet propagation, respectively. Thus, this study reconciles and integrates insights from previous studies on Atlantic blocking events, providing a cohesive understanding of their formation.摘要为研究北大西洋阻高的形成机制, 本文在局部有限振幅波活动 (LWA) 框架下进行了一系列数值实验. 采用的数值模型能显式地描绘出两种重要的大气内部动力过程, 即非线性纬向位涡通量和Rossby波包传播. 模拟结果显示, 这两种动力学过程均是形成大西洋阻高的重要机理. 具体地, 非线性纬向位涡通量和Rossby波包传播, 分别是大西洋阻高南部和北部LWA形成的主导因子. 因此, 本研究综合了前人关于大西洋阻高的研究成果, 为其形成机理提供了新的认识.

Propagation dynamics of self-accelerating second-order Hermite complex-variable-function Gaussian wave packets in a harmonic potential

This paper investigates the evolutionary dynamics of self-accelerating second-order Hermite complex-variable-function Gaussian (SSHCG) wave packets in a harmonic potential. The periodic variation of the wave packets is discussed via theoretical analysis and numerical simulation. The control variables method is applied to manipulate the distribution factor, cross-phase factor, potential depth, and chirp parameter, enabling the realization of unique propagation dynamics. In three-dimensional models, the SSHCG wave packets exhibit rotational states, featuring butterfly shape, three peaks shape, two polarity shape, elliptical shape, and ring-shaped double-vortex structures. Furthermore, the energy flow and the angular momentum of the wave packets are investigated. Additionally, the performance of the radiation force on a Rayleigh dielectric particle is studied. This investigation results in the emergence of distinct SSHCG wave packet propagation dynamics, and potential applications in optical communications and optical trapping are presented.

Wave-Packet Surface Propagation for Light-Induced Molecular Dynamics.

Recent advances in laser technology have enabled tremendous progress in light-induced molecular reactions, at the heart of which the breaking and formation of chemical bonds are located. Such progress has been greatly facilitated by the development of an accurate quantum-mechanical simulation method, which, however, does not necessarily accompany clear dynamical scenarios and is rather computationally heavy. Here, we develop a wave-packet surface propagation (WASP) approach to describe the molecular bond-breaking dynamics from a hybrid quantum-classical perspective. Via the introduction of quantum elements including state transitions and phase accumulations to the Newtonian propagation of the nuclear wave packet, the WASP approach naturally comes with intuitive physical scenarios and accuracies. It is carefully benchmarked with the H_{2}^{+} molecule and is shown to be capable of precisely reproducing experimental observations. The WASP method is promising for the intuitive visualization of light-induced molecular dynamics and is straightforward extensible towards complex molecules.

Application of metric space method in quantum information in quasi-periodic systems

Due to the rapid advancement of quantum information theory, some concepts such as fidelity and entanglement entropy have been introduced into the study of quantum phase transitions, which can be used not only to identify novel matter phases but also to detect the critical point and describe the critical behavior of the quantum phase transitions. From the point of view of the metric space, these physical quantities can be understood as the distance between the two functions in the metric space. In this work, we study a class of quasi-periodic system represented by the generalized Aubry-André-Harper (AAH) model, by using the distance between various wavefunctions or density distribution functions in real space. The generalized AAH model, an ideal platform to understand Anderson localization and other novel quantum phenomena, provides rich phase diagrams including extended, localized, even critical (multifractal) phases and can be realized in a variety of experimental platforms. In the standard AAH model, we find that the extended and localized phases can be identified. In addition, there exists a one-to-one correspondence between two distinct distances. We are able to precisely identify the critical point and compute the critical exponent by fitting the numerical results of different system sizes. In the off-diagonal AAH model, a complete phase diagram including extended phase, localized phase, and critical phase is obtained and the distance of critical phases is intermediate between the localized phase and extended phase. Meanwhile, we apply the metric space method to the wave packet propagation and discover that depending on the phase, the distance between wave functions or density functions exhibits varying dynamical evolution behavior, which is characterized by the exponent of the power-law relationship varying with time. Finally, the distance between the state density distribution functions is proposed, and it effectively identifies distinct matter phases and critical points. The critical phase which displays a multifractal structure, when compared with the other two phases, has the large state density distribution function distance. In a word, by defining the distances of a function under different parameters, we provide not only a physical quantity to identify familiar phase transitions but also an intuitive way to identify different matter phases of unknown systems, phase transition points, and their critical behaviors.