Spreading Of Wave Packet Research Articles

What is ballistic transport?

In this article, we review some notions of ballistic transport from the mathematics and physics literature, describe their basic interrelations, and contrast them with other commonly studied notions of wave packet spread.

Effects of edge disorder on the stability of quantum oscillations in two-dimensional coupled systems

This paper utilizes the theory of quantum diffusion to analyze the electron probability and spreading width of a wavepacket on each layer in a two-dimensional (2D) coupled system with edge disorder, aiming to clarify the effects of edge disorder on the stability of the electron periodic oscillations in 2D coupled systems. Using coupled 2D square lattices with edge disorder as an example, we show that, the electron probability and wavepacket spreading width exhibit periodic oscillations and damped oscillations, respectively, before and after the wavepacket reaches the boundary. Furthermore, these electron oscillations exhibit strong resistance against disorder perturbation with a longer decay time in the regime of large disorder, due to the combined influences of ordered and disordered site energies in the central and edge regions. Finally, we numerically verified the universality of the results through bilayer graphene, demonstrating that this anomalous quantum oscillatory behavior is independent of lattice geometry. Our findings are helpful in designing relevant quantum devices and understanding the influence of edge disorder on the stability of electron periodic oscillations in 2D coupled systems.

Expanding wave packets and the quantum to classical transition

The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.

Quantum isotropic Universe in RQM analogy: The cosmological horizon

We investigate the quantum dynamics of the isotropic Universe in the presence of a free massless scalar field, playing the role of a physical clock. The Hilbert space is constructed via a direct analogy between the Wheeler-DeWitt equation in the minisuperspace and a relativistic scalar one in physical space. In particular, we show how the introduction of a “turning point” in the Universe evolution allows to overcome an intrinsic ambiguity in representing the expanding and collapsing Universe. In this way, the positive and negative frequencies are simply identified with time reversed states. The main subject of the present analysis is the construction of a horizon operator, whose quantum behavior is investigated when Polymer Quantum Mechanics is implemented to describe the asymptotic evolution near the initial singularity. The reason of this choice is motivated by the intrinsic spreading of localized wavepackets when the polymer dispersion relation governs the quantum dynamics. The evidence that the mean value of the quantum horizon operator follows its semiclassical behavior (corrected for polymerization) is a clear indication that a concept of causality can be restored also in the quantum cosmological picture.

Super-ballistic diffusion induced by nonlinear interactions in a one-dimensional quasiperiodic lattice

We numerically investigate the spreading dynamics of wave packets in a one-dimensional lattice with quasiperiodic disorders and nonlinear interactions. Under moderate disorder strength, we reveal an intriguing super-ballistic diffusion driven by increasing the interaction strength from the ballistic diffusion in the non- and weakly interacting cases. We obtain a wide parameter region for such a faster-than-ballistic spreading of wave packets in the quasiperiodic lattice, although the nonlinear self-trapping is dominated under strong interactions. The super-ballistic diffusion is further analyzed based on the point source model. We also show the interaction-induced sub-diffusive spreading in the Anderson localized regime. The super-ballistic and sub-diffusive dynamics are exhibited in the spreading that starts from both the single-site and Gaussian wave packets. Our results showcase the interaction-enabled super-ballistic diffusion, which is scarce and experimentally realizable in artificial atomic or photonic lattices.

Nonspreading relativistic electron wavepacket in a strong laser field

A solution of the Dirac equation in a strong laser field presenting a nonspreading wave packet of the electron is derived. It consists of a generalization of the self-accelerating free electron wavepacket [I. Kaminer , ] to the case with the background of a strong laser field. Built upon the notion of nonspreading for an extended relativistic wavepacket, the concept of Born rigidity for accelerated motion in relativity is the key ingredient of the solution. At its core, the solution comes from the connection between the self-accelerated free electron wavepacket and the eigenstate of a Dirac electron in a constant and homogeneous gravitational field via the equivalence principle. The solution is an essential step towards the realization of the laser-driven relativistic collider [S. Meuren , ], where the large spreading of a common Gaussian wavepacket during the excursion in a strong laser field strongly limits the expectable yields. Published by the American Physical Society 2024

Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds.

We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter λ, and on the other hand our numerics show that it follows a power law for a broad range of values of λ. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

Coherent transient exciton transport in disordered polaritonic wires

Abstract Excitation energy transport can be significantly enhanced by strong light–matter interactions. In the present work, we explore intriguing features of coherent transient exciton wave packet dynamics on a lossless disordered polaritonic wire. Our main results can be understood in terms of the effective exciton group velocity, a new quantity we obtain from the polariton dispersion. Under weak and moderate disorder, we find that the early wave packet spread velocity is controlled by the overlap of the initial exciton momentum distribution and its effective group velocity. Conversely, when disorder is stronger, the initial state is nearly irrelevant, and red-shifted cavities support excitons with greater mobility. Our findings provide guiding principles for optimizing ultrafast coherent exciton transport based on the magnitude of disorder and the polariton dispersion. The presented perspectives may be valuable for understanding and designing new polaritonic platforms for enhanced exciton energy transport.

Revealing violations of macrorealism in flavor oscillations: Leggett-Garg inequalities and no-signaling-in-time conditions

Abstract. We briefly review recent developments in the study of the quantum nature of flavor mixing; in particular, the attention will be devoted to neutrino and neutral meson oscillations. We employ Leggett-Garg type inequalities and no-signaling-in-time conditions to probe the intrinsic quantumness of such a physical manifestation, showing how the analysis is not affected by the wave-packet spreading (for neutrinos) and the intrinsic particle instability (for mesons).

The exotic behavior of the wave evolution in Lévy crystals within a fractional medium

We investigate a traveling Gaussian wave packet transport through a rectangular quantum barrier of lévy crystals in fractional quantum mechanics formalism. We study both standard and fractional Schrödinger equations in linear and nonlinear regimes by using a split-step finite difference (SSFD) method. We evaluate the reflection, trapping, and transmission coefficients of the wave packet and the wave packet spreading by using time-dependent inverse participation ratio (IPR) and second moment. By simultaneously adjusting the fractional and nonlinear terms, we create sharp pulses, which is an essential issue in optoelectronic devices. We illustrate that the effects of barrier height and width on the transmission coefficient are strangely different for the standard and fractional Schrödinger equations. We observe fortunately soliton-like localized wave packets in the fractional regime. Thus, we can effectively control the behavior of the wave evolution by adjusting the available parameters, which can excite new ideas in optics.

Neutrino decoherence and violation of the strong equivalence principle

We analyze the dynamics of neutrino Gaussian wave-packets, the damping of flavor oscillations and decoherence effects within the framework of extended theories of gravity. We show that, when the underlying description of the gravitational interaction admits a violation of the strong equivalence principle, the parameter quantifying such a violation modulates the wave-packet spreading, giving rise to potentially measurable effects in future neutrino experiments.

Asymptotic states for kink–meson scattering

The definition of a quantum state corresponding to a wave packet far from a global soliton is considered. We define an asymptotic quantum state corresponding to a localized wave packet of elementary quanta far from a kink. We demand that the state satisfies two properties. First, it must evolve in time via a rigid translation of the wave packet, up to the usual wave packet spreading and corrections which are exponentially suppressed in the distance to the kink. Second, the state must be invariant under a simultaneous translation of the kink and the wave packet. We explicitly construct the leading quantum corrections to an asymptotic state consisting of a meson approaching a kink. We expect this construction to readily generalize to elementary quanta in the presence of any global soliton.

On free fall of fermions and antifermions

We propose a model describing spin-half quantum particles in curved spacetime in the framework of quantum field theory. Our model is based on embodying Einstein’s equivalence principle and general covariance in the definition of quantum-particle states. With this model at hand, we compute several observables which characterise spin-half quantum particles in a gravitational field. In particular, we find that spin precesses in a normal Fermi frame, even in the absence of torsion. The effect appears to be complementary to free-fall non-universality we have recently reported about for spinless quantum particles. Furthermore, we find that quantum-particle gravitational-potential energy is insensitive to wave-packet spreading in the Earth’s gravitational field, that is responsible for the non-universality of free fall in quantum theory. This theoretical result provides another channel for the experimental study of our quantum-particle model by using gravitational spectrometers. Finally, we also find that (elementary) fermions and antifermions are indistinguishable in gravity.

Interplay of many-body interactions and quasiperiodic disorder in the all-bands-flat diamond chain

We study the effects of quasiperiodic Aubry-Andr\'e (AA) disorder and interactions on a one-dimensional all-band-flat (ABF) diamond chain. We consider the application of disorder in two ways: a symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell, and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. The single-particle wave-packet dynamics for the clean system and when the disorder is applied symmetrically show quantum caging; in the antisymmetric case, the wave-packet spreads over the entire lattice. These results agree with our previous work, where compact localization was observed in the case of the clean system and for symmetrically disordered diamond lattices. In the presence of nearest-neighbour interactions, nonergodic phases are observed in the case of a clean system and symmetrical disorder; at higher disorder strengths, we find an MBL-like phase in the symmetric case. However, many-body non-equilibrium dynamics of the system from carefully engineered initial states exhibit quantum caging. In the antisymmetric case, a nonergodic mixed phase, a thermal phase and an MBL-like phases, respectively, are observed at low, intermediate and high disorder strengths. We observe an absence of caging and initial state dependence (except at the intermediate disorder strength) in the study of non-equilibrium dynamics.

RETRACTED: Non-Hermiticity of tunneling time in a spacetime-symmetric extension of nonrelativistic quantum mechanics

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the classical and relativistic notions of time, where space and time have the same hierarchy, which is essential in describing events in spacetime. On the other hand, in quantum mechanics time appears as a classical parameter, meaning that it does not have an uncertainty relation with its canonical conjugate. In this work, we use a recent spacetime-symmetric proposal [Phys. Rev. A 95, 032133 (2017)] that tries to solve the unbalance in nonrelativistic quantum mechanics by extending the usual Hilbert space, having the time parameter $t$ and the position operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}$ in one subspace and the position parameter $x$ and time operator $\mathbb{T}$ in the other subspace. Time as an operator is better suitable for describing tunneling processes. We then solve the $1/2$-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunneling time through a rectangular barrier. Using a Gaussian energy distribution, we demonstrate that, for wavepackets well resolved in time, the expectation value of the operator $\mathbb{T}$ is the energy average of the classical time ${T}_{\text{class}}=\ensuremath{\partial}S/\ensuremath{\partial}E$, where $S$ is the classical action, which can be real or imaginary. For wavepackets not well resolved in time, the contribution of ${T}_{\text{class}}$ consistently vanishes, and solely properties of the energy distribution contribute to $\mathbb{T}$. We show that the time of travel for nontunneling particles is purely real. When tunneling is involved, complex arrival times emerge, becoming a signature of tunneling. Furthermore, we apply our results to a constant energy distribution, obtaining pure imaginary times for energies below the barrier while obtaining complex times for particles with a wavepacket spreading energies below and above the barrier, and show a comparison to previous works.

Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach

We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet.

Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain

We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of the system are varied, we show that the transition between two different topological phases is preceded by an anomalous diffusion, in contrast to Anderson localization within these topological phases. In the presence of onsite nonlinearity this feature is lost due to mode-mode interactions. Direct numerical simulations reveal that the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space. Our findings underline the importance of mode-mode interactions in nonlinear topological systems, which must be studied in order to define reliable nonlinear topological markers.

Nondipole signatures in ionization and high-order harmonic generation

We analyze nondipole effects arising in ionization and high-order harmonic generation for a two-dimensional hydrogen atom irradiated with either low- or high-frequency laser pulses. In the low-frequency case, the electron wave packet dynamics is dominated by rescattering processes within the laser pulse. Here both odd- and even-order harmonics are generated in the direction of the laser field propagation and polarization, respectively. For high-frequency pulses, such rescattering processes can be neglected. We demonstrate that a significant portion of photoelectrons is detected opposite to the laser pulse propagation direction as a consequence of their postpulse wave packet spreading and interaction with the parent ion. This is accompanied by rich interference structures formed in the momentum distributions of photoelectrons. Our results follow from the numerical solution of the time-dependent Schr\"odinger equation, which is based on the Suzuki-Trotter scheme with the split-step Fourier approach. The method relies on a Hamiltonian decomposition, where except for the components depending exclusively on the momentum or on the position operators, there are also terms depending on both momentum and position operators in particular configurations. We demonstrate that, as long as the latter does not depend on noncommuting coordinates of the momentum and position operators, nondipole effects in laser-matter interactions can be studied without applying extra approximations and unitary operations.

Forward-propagation-free focusing MUSIC algorithm for Lamb waves

The multiple signal classification (MUSIC) algorithm is originally used for direction of arrival estimation and frequency identification. MUSIC-like algorithms have gained their popularity in structural health monitoring (SHM) owing to their super-resolution characteristic and the virtue of baseline independence. MUSIC essentially is a searching algorithm to find the best phase difference matching between the eigenvector from signal subspace and the presupposed steering vector. However, in the guided-wave-based SHM (in plate-like structure, the guided wave is Lamb wave), the dispersion effect will definitely lead to phase distortion. Therefore, Xu et al. presented a focusing MUSIC algorithm where the time reversal technique is adopted to eliminate the dispersion in the way of back propagation. Seeing that the phase difference information, which is necessary for MUSIC, disappears after back propagation, the damage scattered wave packet, obtained by window truncation, is forward propagated again at the constant group velocity to recover the time of flight information. Nevertheless, the forward propagation process is superfluous from the view of phase matching. In the presented forward-propagation-free focusing MUSIC (FPF-F MUSIC) algorithm (the simplified version of Xu’s work), by revising the steering vector in the form of phase coincidence, the matching relation for MUSIC is modified from phase difference matching to phase alignment matching, so that the forward propagation and the steering vector traversal setting for every inspection point are all omitted. The damage localization performance of FPF-F MUSIC is verified on the aluminum plate with double through-hole and surface defects under uniform linear and circular arrays.

Simulation of the electron trajectories by ultrashort high intensity linearly polarized two lasers to improve the harmonics generation in plasmas

A numerical simulation based on the one and two-dimensional semi-classical model and the tunnelling ionization process was investigated. The influence of the laser electric field on the paths of an electron and the laser magnetic field on the longitudinal drift of the electron was calculated. The electron trajectories in ultrahigh intensity laser were studied in this simulation, the laser field was polarized in the x-direction and propagated in the z-direction. The spreading of electron wave-packet in a continuum was taken into account, and the energy of the generated harmonic photon was estimated by this simulation. A new method to optimize the harmonic photons by controlling the tunnelling ionization and correcting the longitudinal drift of an electron was suggested. This new method utilized two orthogonal linearly-polarized laser beams with a suitable phase difference. It was found that; two counter-propagating laser beams can also decrease the longitudinal drift of the electron and increase the probability of harmonic photons generation.