Behavior Of Wave Packets Research Articles

Wavepacket dynamics of the excited (S1) state of 2,5-difluoroaniline by accidental resonance with the Rydberg states.

Coherent nuclear wavepacket behavior obtained by time-resolved spectroscopy is a good choice to capture the real-time evolution of molecular configuration. Using femtosecond time-resolved photoelectron imaging, we investigate the real-time evolution of the vibrational wavepacket of 2,5-difluoroaniline following the coherent excitation of an out-of-plane vibrational mode in the S1 state at 289.8nm. Probed by an accidental resonance with the Rydberg states, the periodic oscillations with the frequency of 99cm-1 are observed from the photoelectron kinetic energy (PKE) distributions, corresponding to the energy difference between the out-of-plane mode X1 0 of C-F bond and the band origin. Moreover, phase reversal of π rad between 0.66-0.75 and 1.00-1.08eV is also observed in the PKE region. Combined with the scan of the potential energy surface in the ground cationic D0 state, the observed two ionization channels corresponding to different phases are attributed to the periodic geometry changes between the planar and the non-planar structures when the coherent wavepacket evolves from the initial vertical Franck-Condon region toward the global minimum of the S1 potential energy surface.

Wave-packet behaviors of the defocusing nonlinear Schrödinger equation based on the modified physics-informed neural networks.

Investigated in this paper is the defocusing nonlinear Schrödinger (NLS) equation, which is used for describing the wave-packet dynamics in certain weakly nonlinear media. With the physics-informed neural networks (PINNs), we modify the corresponding loss function in the existing literature and obtain two types of dark solitons, type-I and type-II solitons. It is demonstrated that the modified loss function presents higher-precision wave-packet behaviors based on fewer initial and boundary data. Taking type-I solitons into consideration, we find that when only a small fraction of initial and boundary data are given, the prediction accuracy of the wave packets will be increased one or two orders of magnitude at least if the modification term of the loss function is introduced. Furthermore, for the inverse problem, the modified loss function provides a better estimate of the nonlinear coefficient of the NLS equation based on fewer observed data of the wave packets. For type-II solitons, we compare the required data and predicted results of the PINNs with those of the conventional time-splitting finite difference (TSFD) method and reveal that achieving the same precision of the wave-packet behavior, the PINNs with the modified loss functions require only one tenth of the amount of the initial and boundary data of the TSFD method. Besides, both unmodified and modified loss functions are exploited for predicting the behaviors of Gaussian wave packets, and it is observed that the predicted result of the modified loss function agrees with the high-precision solution of the time-splitting Fourier pseudospectral method, whereas the unmodified loss function fails.

The impact of memory effect on space fractional strong quantum couplers with tunable decay behavior and its numerical simulation

The nontrivial behavior of wave packets in the space fractional coupled nonlinear Schrödinger equation has received considerable theoretical attention. The difficulty comes from the fact that the Riesz fractional derivative is inherently a prehistorical operator. In contrast, nonlinear Schrödinger equation with both time and space nonlocal operators, which is the cornerstone in the modeling of a new type of fractional quantum couplers, is still in high demand of attention. This paper is devoted to numerically study the propagation of solitons through a new type of quantum couplers which can be called time-space fractional quantum couplers. The numerical methodology is based on the finite-difference/Galerkin Legendre spectral method with an easy to implement numerical algorithm. The time-fractional derivative is considered to describe the decay behavior and the nonlocal memory of the model. We conduct numerical simulations to observe the performance of the tunable decay and the sharpness behavior of the time-space fractional strongly coupled nonlinear Schrödinger model as well as the performance of the numerical algorithm. Numerical simulations show that the time and space fractional-order operators control the decay behavior or the memory and the sharpness of the interface and undergo a seamless transition of the fractional-order parameters.

Particlelike Behavior of Topological Defects in Linear Wave Packets in Photonic Graphene.

Topological defects, such as quantum vortices, determine the properties of quantum fluids. Their study has been at the center of activity in solid state and BEC communities. In parallel, the nontrivial behavior of linear wave packets with complex phase patterns was investigated by singular optics. Here, we study the formation, evolution, and interaction of optical vortices in wave packets at the Dirac point in photonic graphene. We show that while their exact behavior goes beyond the Dirac equation and requires a full account of the lattice properties, it can be still approximately described by an effective theory considering the phase singularities as "particles". These particles are capable of mutual interaction, with their trajectory obeying the laws of dynamics.

Synthesizing broadband propagation-invariant space-time wave packets using transmissive phase plates.

Space-time wave packets are a class of pulsed optical beams that are diffraction-free and dispersion-free in free space by virtue of introducing a tight correlation between the spatial and temporal degrees of freedom of the field. Such wave packets have been recently synthesized in a novel configuration that makes use of a spatial light modulator to realize the required spatio-temporal correlations. This arrangement combines pulse-modulation and beam-shaping to assign one spatial frequency to each wavelength according to a prescribed correlation function. Relying on a spatial light modulator results in several limitations by virtue of their pixelation, small area, and low energy-handling capability. Here we demonstrate the synthesis of space-time wave packets with one spatial dimension kept uniform - that is, light sheets - using transparent transmissive phase plates produced by a gray-scale lithography process. We confirm the diffraction-free behavior of wave packets having a bandwidth of 0.25 nm (filtered from a typical femtosecond Ti:sapphire laser) and 30 nm (a multi-terawatt femtosecond laser). This work paves the way for developing versatile high-energy light bullets for applications in nonlinear optics and laser machining.

Characteristics of the spontaneous emission field and spectrum of a two-level atom in a dynamic photonic crystal

The spontaneous emission field and spectrum of a two-level atom, located in an isotropic photonic crystal with dynamic band edges, are investigated by means of numeric calculation. The investigation is expected to help comprehend the characteristics of the atomic spontaneous emission in the dynamic photonic crystal, and provide a possible way to control dynamically the spontaneous emission in photonic crystal. The expression of the spontaneous radiation field is obtained without using the far-zone approximation and the Weisskopf-Wigner approximation, and expected to be applicable in other relevant researches. In the investigation, the spontaneous radiation field and spectrum are calculated when the band edge frequency is unmodulated, or modulated by a step function or triangle function. In the unmodulated situation, the radiation field intensity tends to a constant which is equal to the intensity of the localized field component. The radiation field pulse presents a wave packet behavior as propagation distance increases. The components of the radiation field correspond one-to-one to the peaks in the spontaneous radiation spectrum. When the band edge frequency is modulated by step function, the radiation field intensity tends to a steady-state value after the modulation has happened. And the steady-state intensity is affected by the time when the modulation happens. The components of the non-localized field and the frequency of the localized field after modulation depend on the atomic transition frequency and the band edge frequency, and are identical to those in the unmodulated situation with the same parameters. When the band edge frequency is modulated by a triangle function, the field intensity presents a decaying quasi-periodic oscillation after a long enough time. The modulation frequency determines the frequency of the oscillation, and influences the decay rate. The radiation energy becomes sharp peaks around a set of the discrete frequencies which are evenly spaced with the modulation frequency. The central frequency of these frequencies depends on the atomic transition frequency and the value range of the band edge frequency. The modulation initial phase affects the intensity of the radiation field emitted in an initial period of time.

Semiclassical and quantum behavior of the mixmaster model in the polymer approach

We analyze the quantum dynamics of the Bianchi Type IX model, as described in the so-called polymer representation of quantum mechanics, to characterize the modifications that a discrete na- ture in the anisotropy variables of the Universe induces on the morphology of the cosmological sin- gularity. We first perform a semiclassical analysis, to be regarded as the zeroth-order approximation of a WKB (Wentzel-Kramers-Brillouin) approximation of the quantum dynamics, and demonstrate how the features of polymer quantum mechanics are able to remove the chaotic properties of the Bianchi IX dynamics. Then, we address the study of the full quantum dynamics of this model in the polymer representation and analyze the two cases, in which the Bianchi IX spatial curvature does not affect the wave-packet behavior, as well as the instance, for which it plays the role of an infinite potential confining the dynamics of the anisotropic variables. The main development of this analysis consists of investigating how, differently from the standard canonical quantum evolution, the high quantum number states are not preserved arbitrarily close to the cosmological singularity. This property emerges as a consequence, on one hand, of the no longer chaotic features of the classical dynamics (on which the Misner analysis is grounded), and, on the other hand, of the impossibility to remove the quantum effect due to the spatial curvature. In the polymer picture, the quantum evolution of the Bianchi IX model remains always significantly far from the semiclassical behavior, as far as both the wave-packet spread and the occupation quantum numbers are concerned. As a result, from a quantum point of view, the Mixmaster dynamics loses any predictivity characterization for the discrete nature of the Universe anisotropy.

Determination of photodissociation and radiative association cross sections from the same time-dependent calculation

We illustrate some of the difficulties that may be encountered when computing photodissociation and radiative association cross sections from the same time-dependent approach based on wavepacket propagation. The total and partial photodissociation cross sections from the 33 vibrational levels of the b 3Σ+ state of HeH+ towards the nine other 3Σ+ and 6 3Π n = 2, 3 higher lying electronic states are calculated, using the autocorrelation method introduced by Heller (1978 J. Chem. Phys. 68 3891) and the method based on the asymptotic behaviour of wavepackets introduced by Balint-Kurti et al (1990 J. Chem. Soc. Faraday Trans. 86 1741). The corresponding radiative association cross sections are extracted from the same calculations, and the photodissociation and radiative association rate constants are determined.

Robust dynamical recurrences based on Floquet spectrum

Recurrence behavior of wave packets in coupled higher dimensional systems and periodically driven systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to nonlinear resonances developed in the systems and provide the analytical understanding of recurrence times.We apply these analytical results to investigate the recurrence times of matter waves in optical lattice in the presence of external periodic forcing. The obtained analytical results can experimentally be observed using currently available experimental setups.

DNS of wavepacket evolution in a Blasius boundary layer

This paper presents the direct numerical simulation (DNS) of wavepacket evolution and breakdown in a Blasius boundary layer. The study covers the physical, spectral and structural aspects of the whole transition process, whereas previous studies have tended to focus on issues of a more limited scope. The simulations are modelled after the experiments of Cohen, Breuer & Haritonidis (J. Fluid Mech., vol. 225, 1991, p. 575). The disturbance wavepackets are initiated here by au-velocity and av-velocity delta pulse. They evolve through a quasi-linear growth stage, a subharmonic stage and a strongly nonlinear stage before breaking down into the nascent turbulent spots. Pulse-initiated wavepackets provide a plausible model for naturally occurring laminar–turbulent transition because they contain disturbances in a broadband of frequencies and wavenumbers, whose sum of interactions determines the spatio-temporal progress of the wavepackets. The early development of the wavepackets accords well with established linear results. The ensuing subharmonic evolution of the wavepackets appears to be underpinned by a critical-layer-based mechanism in which thex-phase speeds of the fundamental two-dimensional and dominant three-dimensional waves with compatible Squire wavenumbers are approximately matched. Spectral data over the bulk of the subharmonic stage demonstrate good consistency with the action of a phase-locked theory recently proposed by Wu, Stewart & Cowley (J. Fluid Mech., vol. 590, 2007, p. 265), strongly suggesting that the latter may be the dominant mechanism in the broadband nonlinear evolution of wavepackets. The dominant two-dimensional and three-dimensional waves are observed to be spontaneously evolving towards triad resonance in the late subharmonic stage. The simulations reproduce many key features in the experiments of Cohenet al. (1991) and Medeiros & Gaster (J. Fluid Mech., vol. 399, 1999b, p. 301). A plausible explanation is also offered for the apparently ‘deterministic’ subharmonic behaviour of wavepackets observed by Medeiros & Gaster. The strongly nonlinear stage is signified by the appearance of low-frequency streamwise-alignedu-velocity structures at twice the spanwise wavenumber of the dominant three-dimensional waves, distortion of the local base flow by the strengthening primary Λ-vortex and rapid expansion of the spanwise wavenumber (β) spectrum. These are in broad agreement with the experimental observations of Breuer, Cohen & Haritonidis (J. Fluid Mech., vol. 340, 1997, p. 395). The breakdown into incipient turbulent spots occurs at locations consistent with the experiments of Cohenet al. (1991). A visualization shows that the evolving wavepackets comprise very thin overlapping vorticity sheets of alternating signs, in stacks of two or three. Strong streamwise stretching of the flow at the centre of the wavepacket in the late subharmonic and strongly nonlinear stages promotes the roll-up and intensification of the vorticity sheets into longitudinal vortices, whose mutual induction precedes the breakdown of the wavepacket. The critical layer of the dominant two-dimensional and oblique wave modes reveals the progressive coalescence of a strong pair of vortices (associated with the Λ-vortex) during the subharmonic stage. Their coalescence culminates in a strong upward burst of velocity that transports lower momentum fluid from below the critical layer into the upper boundary layer to form a high shear layer in the post-subharmonic stage.

Fractional revivals through Rényi uncertainty relations

We show that the R\'enyi uncertainty relations give a good description of the dynamical behavior of wave packets and constitute a sound approach to revival phenomena by analyzing three model systems: the simple harmonic oscillator, the infinite square well, and the quantum bouncer. We prove the usefulness of entropic uncertainty relations as a tool for identifying fractional revivals by providing a comparison in different contexts with the usual Heisenberg uncertainty relation and with the common approach in terms of the autocorrelation function.

Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

We consider the nonlinear Schrodinger equation with an integral Hartree-type nonlinearity in a thin quantum waveguide and study the propagation of Gaussian wave packets localized in the spatial variables. In the case of periodically varying waveguide walls, we establish the relation between the behavior of wave packets and the spectral properties of the auxiliary periodic problem for the one-dimensional Schrodinger equation. We show that for a positive value of the nonlinearity parameter, the integral nonlinearity prevents the packet from spreading as it propagates. In addition, we find situations such that the packet is strongly focused periodically in time and space.

Quantum phantom cosmology

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.

Selective observation of the wave-packet dynamics in the excited states at KBrFcenters by luminescence experiments

We investigated temporal evolutions of the luminescence spectra in KBr $F$ centers at $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using the up-conversion spectroscopy method, and observed damped wave-packet oscillation on the adiabatic potential-energy surface in the excited state. The wave-packet behavior is quite different from that observed through previous pump-probe measurements. The result shows that in the excited state the vacancy trapped electron interacts predominantly with the bulk phonon modes, in contrast to the ground state where it couples mainly to the ${A}_{1g}$ local mode.

Influence of centrifugal forces on the development of wave packets in boundary layers with a uniformly valid model

The behavior of three-dimensional wave packets in the boundary layer on curved surfaces is analyzed in this study based on a modification of the triple-deck theory referred to as the “criss-cross” interaction model. The equations of the criss-cross interaction describe a particular type of boundary layer instability mode that possesses underlying properties of both the Tollmien–Schlichting waves and Taylor–Görtler vortices. Previous analysis of the criss-cross interaction regime suggests a possibility for upstream propagation of perturbations in the boundary layer and possible absolute instability of the flow. However, these results cannot be considered as conclusive because the initial-value problem for the criss-cross interaction equations is ill-posed. In a recent work [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid–viscous interaction theory. Stud Appl Math 2002;108:161–85] a regularized non-asymptotic model to describe criss-cross interaction has been proposed. Whereas in the original version of the theory, perturbations have an unbounded growth rate as the longitudinal wave number ∣ k∣ → ∞, in the new model of [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid–viscous interaction theory. Stud Appl Math 2002;108:161–85], as physically expected the amplification rate remains bounded for both spatially growing and temporally growing waves. A Fourier transform method is used in the present study to solve the linearized equations for the flow over concave roughness and humps and it is found that disturbances develop and are convected downstream as wave packets. The behavior of the wave packets is consistent with convective instability, and the upstream influence is no longer present at large times.

Initial states and the various long-time-behaviors of the unstable multilevel systems

Initial states and the various long-time-behaviors of the unstable multilevel systems

Beyond the veil: Inner horizon instability and holography

We show that scalar perturbations of the eternal, rotating Banados-Teitelboim-Zanelli (BTZ) black hole should lead to an instability of the inner (Cauchy) horizon, preserving strong cosmic censorship. Because of backscattering from the geometry, plane-wave modes have a divergent stress tensor at the event horizon, but suitable wave packets avoid this difficulty, and are dominated at late times by quasinormal behavior. The wave packets have cuts in the complexified coordinate plane that are controlled by requirements of continuity, single-valuedness, and positive energy. Due to a focusing effect, regular wave packets nevertheless have a divergent stress energy at the inner horizon, signaling an instability. We propose that this instability, which is localized behind the event horizon, is detected holographically as a breakdown in the semiclassical computation of dual conformal field theory (CFT) expectation values in which the analytic behavior of wave packets in the complexified coordinate plane plays an integral role. In the dual field theory, this is interpreted as an encoding of physics behind the horizon in the entanglement between otherwise independent CFTs.

Wave packet dynamics along bifurcating reaction paths

The problem of bifurcating reaction paths is revisited by wave packet (WP) dynamics. The pitchfork model connecting five stationary points—a reactive, two transition structures and two enantiomeric products—is characterized by a Valley Ridge inflection point (VRI) where WP could leave the standard intrinsic reaction path. We question the role of such a VRI point to determine whether the mechanism is sequential or concerted. WP simulations on two-dimensional minimum energy surfaces are carried out in the benchmark case of the methoxy radical isomerization H3CO→H2COH. The ab initio potential energy surface (PES) is fitted to an analytical model which is bent to analyze the incidence of geometrical parameters on the WP behavior. For each of these generated PES, the WP width in the entrance valley is the main factor which conditions the behavior on the unstable ridge. The WP evolution is also analyzed in terms of nonadiabatic transitions among adiabatic channels along the reaction coordinate. Finally, the location of VRI points according to an invariant definition is discussed.

Quantum Mechanical Analysis of the Equilateral Triangle Billiard: Periodic Orbit Theory and Wave Packet Revivals

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by Trev=9μa2/4ħπ where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°–60°–60°) triangle, such as the half equilateral (30°–60°–90°) triangle and other “foldings,” which have related energy spectra and revival structures.

Mach-Zehnder interferometer for a two-photon wave packet

We propose an experiment that permits observation of the de Broglie two-photon wave packet behavior for a pair of photons, using a Mach-Zehnder interferometer. It is based on the use of pulsed lasers to generate pairs of photons via spontaneous parametric down-conversion and the post-selection of events. It differs from previous realizations by the use of a third time-correlated photon to engineer the state of the photons. The same technique can give us which-path information via an ``interaction-free'' experiment and can be used in other experiments on the foundations of quantum mechanics related to wave-particle duality and to nonlocality.