Finite Wave Packets Research Articles

Broad sterile neutrinos & the reactor/gallium tension

Significant evidence exists for the apparent disappearance of electron-type neutrinos in radioactive source experiments. Yet, interpreted within the standard ‘3+1 sterile neutrino scenario’, precision short-baseline measurements of electron antineutrinos from nuclear reactors strongly disagree with these results. Recently, it has been demonstrated that allowing for a finite wavepacket size for the reactor neutrinos can ameliorate such a tension, however the smallness of the required wavepackets is a subject of intense debate. In this work, we demonstrate that a ‘broad’ sterile neutrino may relax this tension in much the same way. Such a phenomenological possibility can arise in plausible hidden sector scenarios, such as a clockwork-style sector, for which we provide a concrete microscopic model.

Confronting solutions of the Gallium Anomaly with reactor rate data

Recently, several models have been suggested to reduce the tension between Gallium and reactor antineutrino spectral ratio data which is found in the framework of 3+1 active-sterile neutrino mixing. Among these models, we consider the extensions of 3+1 mixing with a finite wavepacket size, or the decay of the heaviest neutrino ν4, or the possibility to have a broad ν4 mass distribution. We consider the reactor antineutrino rate data and we show that these models cannot eliminate the tension between Gallium and reactor rate data that is found in the 3+1 neutrino mixing framework. Indeed, we show that the parameter goodness of fit remains small. We consider also a model which explains the Gallium Anomaly with non-standard decoherence in the framework of three-neutrino mixing. We find that it is compatible with the reactor rate data.

A modal decomposition approach to topological wave propagation

The design of valley-Hall topological insulators is typically informed by analyzing the primitive unit cell, using the Berry curvature of the Bloch-eigenmodes to predict energy localization on the domain boundary, or the dispersion diagram of the semi-infinite lattice to predict the group velocity of topological waves. However, practical systems are finite in size and the propagating topological wave is composed of a finite bandwidth as guaranteed by the Fourier uncertainty principle. Hence, the propagation predicted by the ideally infinite lattice for a given frequency deviate from practical topological systems driven by finite bandwidth wave packets. In this work, we demonstrate that the propagating topological waves in valley Hall lattices can be interpreted using the linear degenerate modal basis. We show that a small subset of closely spaced modes comprise the topological waves, which enables the construction of analytical reduced-order models that accurately capture the topological wave. This result is related to the sparse density of the modal spectrum inside the topological band gap, which allows for the energy to be carried nearly completely by a narrow band of spectrally isolated eigenmodes that are spatially localized along the domain boundary. This result is then employed to refine group velocity predictions of propagating topological waves with respect to input signal bandwidth and frequency by matching the modal spectrum to the supercell dispersion diagram describing the semi-infinite system. Moreover, we utilize the damped modal spectrum to characterize variations in wave group velocity in damped topological lattices and predict edge-to-bulk transitions. Hence, this work establishes a framework for accurately characterizing undamped and damped topological wave propagation in quantum valley Hall systems using the machinery of classical dynamics.

Impact of wave packet separation in low-energy sterile neutrino searches

Light sterile neutrinos have been motivated by anomalies observed in short-baseline neutrino experiments.Among them, radioactive-source and reactor experiments have provided evidence and constraints, respectively, for electron neutrino disappearance compatible with an eV-scale neutrino. The results from these observations are seemingly in conflict. This letter brings into focus the assumption that the neutrino wave packet can be approximated as a plane wave, which is adopted in all analyses of such experiments. We demonstrate that the damping of oscillations, e.g., due to a finite wave packet size, solve the tension between these electron-flavor observations and constraints.

Neutrino decoherence and the mass hierarchy in the JUNO experiment

The finite size of a neutrino wavepacket at creation can affect its oscillation probability. Here, we consider the electron antineutrino wavepacket and decoherence in the context of the nuclear reactor based experiment JUNO. Given JUNO's high expected statistics [$\sim$100k IBD events ($\bar{\nu}_e p \rightarrow e^+ n$)], long baseline ($\sim$53\,km), and excellent energy resolution [$\sim$$0.03/\sqrt{E_{\mathrm{vis}}~\mathrm{(MeV)}}$], its sensitivity to the size of the wavepacket is expected to be quite strong. Unfortunately, this sensitivity may weaken the experiment's ability to measure the orientation of the neutrino mass hierarchy for currently allowed values of the wavepacket size. Here, we report both the JUNO experiment's ability to determine the hierarchy orientation in the presence of a finite wavepacket and its simultaneous sensitivity to size of the wavepacket and the hierarchy. We find that wavepacket effects are relevant for the hierarchy determination up to nearly two orders of magnitude above the current experimental lower limit on the size, noting that there is no theoretical consensus on the expectation of this value. We also consider the effect in the context of other aspects of JUNO's nominal three-neutrino oscillation measurement physics program and the prospect of future enhancements to sensitivity, including from precise measurements of $\Delta m^2_{3l}$ and a near detector.

Wavelets for the space-time structure analysis of physical fields

Spectral analysis, based on the Fourier method, is a general tool in physics. Wavelets appeared as a natural generalization of classical spectral analysis to the case of complex nonstationary and spatially inhomogeneous systems, for which a comparison with an infinite sinusoid, which forms the basis of the Fourier method, has to be replaced by a comparison with a finite wave packet, which is known as a wavelet. In this review, the authors, based largely on their own experience of application wavelet analysis in astro- and geophysics, solar-terrestrial relations, as well as climatology, medical physics, and laboratory hydrodynamic experiments, demonstrate the possibilities and discuss the practical aspects of the application of the wavelet apparatus to the interpretation of signals and images of various physical natures.

On the need for soft dressing

In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this result in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

Finite equal norm Parseval wavelet frames over prime fields

In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator, we derive a locally-scaled version of the DFT of system generator and obtain a finite equal-norm Parseval wavelet frame over prime fields. We also give a characterization of all multiplicative subgroups of the cyclic multiplicative group, for which the associated wavelet systems form frames. Finally, we present some concrete examples as applications of our results.

Wigner translations and the observer dependence of the position of massless spinning particles.

The Wigner little group for massless particles is isomorphic to the Euclidean group SE(2). Applied to momentum eigenstates, or to infinite plane waves, the Euclidean "Wigner translations" act as the identity. We show that when applied to finite wave packets, the translation generators move the packet trajectory parallel to itself through a distance proportional to the particle's helicity. We relate this effect to the spin Hall effect of light and to the Lorentz-frame dependence of the position of a massless spinning particle.

Wave Packet Transform over Finite Fields

In this article we introduce the notion of finite wave packet groups over finite fields as the finite group of dilations, translations, and modulations. Then we will present a unified theoretical linear algebra approach to the theory of wave packet transform (WPT) over finite fields. It is shown that each vector defined over a finite field can be represented as a coherent sum of finite wave packet group elements as well.

Forces in Aharonov–Bohm optical setting

The Aharonov–Bohm effect is usually associated with a path-dependent phase accumulated by a charged matter wave and determined by an effective vector potential. In a more general geometrical framework, such phase alterations have been the hallmark of a host of related phenomena in many different fields. However, besides phase changes, it was suggested that for finite wave-packets there is also an additional deflection leading to observable changes in the wave’s canonical momentum. In this paper, we create an optical scattering situation that permits observing nonconservative reaction forces, which result from the conservation of canonical momentum. We demonstrate experimentally, for the first time, the presence of such mechanical forces with the magnitude and direction determined by the phase dislocation of the vortex state. Our experimental results offer insights into essentially untested phenomena, where forces act on vortex fields, and allow examining the role of conservation laws and symmetries in complex interacting systems.

Cyclic wave packet transform on finite Abelian groups of prime order

In this paper, we introduce the notion of finite wave packet groups for positive prime integers, as groups of cyclic dilations, translations and modulations. We will present a unified group theoretical approach for the cyclic wave packet transform on finite Abelian groups of prime order. Then, we study basic properties of this windowed transform.

On Quantum Cosmology of the <em>R</em><sup>2</sup> Gravity Theory

We study the minisuperspace quantization of the theory of gravity where an R 2 term is included in the Einstein Hilbert action. Matter is described by a perfect fluid and we employ the generally relativistic hydrodynamic formulation of Schutz. We set up the Wheeler-DeWitt equation and obtain its solutions. A finite norm wave packet solution is constructed and used to calculate asymptotic values for the expectation values of the scale factor and the Ricci scalar

Atomic antenna: Nonlinear scattering of a superatomic-intensity laser pulse

A semiclassical model of high harmonic generation upon ionization by suppressing the atomic barrier is developed. The spreading of the wave packet of an ionized electron, which is chosen in the form of a Gaussian distribution, is considered. The quantum nature of the process is taken into account by the initial discrete level of the electron, and the finite wave packet spreading occurs in the continuum. After its detachment from the atom, the electron is assumed to be free and moving under the action of the laser pulse field and the Coulomb interaction of the electron with the atomic core can be treated as a perturbation. The radiation from the electron is calculated from its acceleration expressed in terms of the average force of interaction of the electron with the Coulomb center of the atom.

Inertia-gravity waves beyond the inertial latitude. Part 1. Inviscid singular focusing

The paper is concerned with analytical study of inertia-gravity waves in rotating density-stratified ideal fluid confined in a spherical shell. It primarily aims at clarifying the possible role of these motions in deep ocean mixing. Recently, it was found that on the ‘non-traditional’ β-plane inertia-gravity internal waves can propagate polewards beyond their inertial latitude, where the wave frequency equals the local Coriolis parameter, by turning into subinertial modes trapped in the narrowing waveguides around the local minima of buoyancy frequencyN. The behaviour of characteristics was established: wave horizontal and vertical scales decrease as the wave advances polewards and tend to zero at a latitude corresponding to an attractor of characteristics. However, the basic questions about wave evolution, its quantitative description and the possibility of its reflection from the critical latitude remain open. The present work addresses these issues by studying the linear inviscid evolution of finite bandwidth wavepackets on the ‘non-traditional’ β-plane past the inertial latitude for generic oceanic stratification. Beyond the inertial latitude, the wave field is confined in narrowing waveguides of three distinct generic types around different local minima of the buoyancy frequency. In the oceanic context, the widest is adjacent to the flat bottom, the thinnest is the upper mixed layer, and the middle one is located between the seasonal and main thermocline. We find explicit asymptotic solutions describing the wave field in the WKB approximation. As a byproduct, the conservation of wave action principle is explicitly formulated for all types of internal waves on the ‘non-traditional’ β-plane. The wave velocities and vertical shear tend to infinity and become singular at the attractor latitude or its vicinity for both monochromatic and finite bandwidth packets. We call this phenomenonsingular focusing. These WKB solutions are shown to remain valid up to singularity for the bottom and mid-ocean waveguides. The main conclusion is that even in the inviscid setting the wave evolution towards smaller and smaller horizontal and vertical scales is irreversible: there is no reflection. For situations typical of deep ocean, a simultaneous increase in wave amplitude and decrease of vertical scale causes a sharp increase of vertical shear, which may lead to wave breaking and increased mixing.

Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates

This paper investigates the characteristics of the second harmonic generation of Lamb waves in a plate with quadratic nonlinearity. Analytical asymptotic solutions to Lamb waves are first obtained through the use of a perturbation method. Then, based on a careful analysis of these asymptotic solutions, it is shown that the cross-modal generation of a symmetric second harmonic mode by an antisymmetric primary mode is possible. These solutions also demonstrate that modes showing internal resonance-nonzero power flux to the second harmonic mode, plus phase velocity matching-are most useful for measurements. In addition, when using finite wave packets, which is the case in most experimental measurements, group velocity matching is required for a cumulative increase in the second harmonic amplitude with propagation distance. Finally, five mode types (which are independent of material properties) that satisfy all three requirements for this cumulative increase in second harmonic amplitude-nonzero power flux, plus phase and group velocity matching-are identified. These results are important for the development of an experimental procedure to measure material nonlinearity with Lamb waves.

Mean flow generated by an internal wave packet impinging on the interface between two layers of fluid with continuous density

Internal waves propagating in an idealized two-layer atmosphere are studied numerically. The governing equations are the inviscid anelastic equations for a perfect gas atmosphere. The numerical formulation eliminates all variables in the linear terms except vertical velocity, which are then treated implicitly. Nonlinear terms are treated explicitly. The basic state is a two-layer flow with continuous density at the interface. Each layer has a unique constant for the Brunt–Vaisala frequency. Waves are forced at the bottom of the domain, are periodic in the horizontal direction, and form a finite wave packet in the vertical. The results show that the wave packet forms a mean flow that is confined to the interface region that persists long after the wave packet has moved away. Large-amplitude waves are forced to break beneath the interface.

Tunneling-time calculations for general finite wave packets based on the presence-time formalism

We analyze the tunneling time problem via the presence time formalism. With this method we reproduce previous results for very long wavepackets and we are able to calculate the tunneling time for general wavepackets of arbitrary shape and length. The tunneling time for a general wavepacket is equal to the average over the energy components of the standard phase time. With this approach we can also calculate the time uncertainty. We have checked that the results obtained with this approach agree extremely well with numerical simulations of the wavepacket evolution.

Nonlinear Propagation of Wave Packets for Near-Critical Wave Numbers in a Liquid that Is Piecewise Nonuniform with Depth

This is a study of the evolution of finite amplitude wave packets at the contact surface between a semi-infinite liquid medium and a liquid located above it near a solid lid. The limiting case of near-critical wave numbers for propagation of wave packets in the liquid system is discussed. Perturbation expansions are obtained for the deviation of the contact surface from its unperturbed position and for wave numbers near the critical value. This is compared with the solution for the analogous limiting cases of one or two semi-infinite liquids. A version in which the wave numbers are far from critical is examined.

Radiative falloff in neutron star spacetimes

We systematically study late-time tails of scalar waves propagating in neutron star spacetimes. We consider uniform density neutron stars, for which the background spacetime is analytic and the compaction of the star can be varied continously between the Newtonian limit 2M/R << 1 and the relativistic Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off neutron stars of different compactions 2M/R and find that a Newtonian, an intermediate, and a highly relativistic regime can be clearly distinguished. In the highly relativistic regime, the reflected signal is dominated by quasi-periodic peaks, which originate from the wave packet bouncing back and forth between the center of the star and the maximum of the background curvature potential at R ~ 3 M. Between these peaks, the field decays according to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between the center and the maximum or the curvature potential grows without bound, so that the first peak arrives only at infinitely late time. The modes of neutron stars can therefore no longer be excited in the ultra-relativistic limit, and it is in this sense that the late-time radiative decay from neutron stars looses all its features and gives rise to power-law tails reminiscent of Schwarzschild black holes.