Vacuum Wave Research Articles

The quantum Gaussian-Schell model: a link between classical and quantum optics.

The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wave packets. This situation prevails for partially coherent light, the most common kind of classical light. Here, for the first time, to our knowledge, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model (GSM) unveils the possibility of performing photon-number-resolving (PNR) detection to isolate the constituent quantum multiphoton wave packets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wave packets with up to 16 photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects but also establish a fundamental bridge between the classical and quantum worlds.

Conformally related vacuum gravitational waves and their symmetries

A special conformal transformation which carries a vacuum gravitational wave into another vacuum one is built by using Möbius-redefined time. It can either transform a globally defined vacuum wave into a vacuum sandwich wave, or carry the gravitational wave into itself. The first type, illustrated by linearly and circularly polarised vacuum plane gravitational waves, permutes the symmetries and the geodesics. Our second type is a pp wave with conformal O(1, 2) symmetry. An example inspired by molecular physics which seems to have escaped attention so far is an anisotropic generalisation of the familiar inverse-square profile and is reminiscent of Aichelburg-Sexl ultraboosts. The particle can escape, or perform circular periodic motion, or fall into the singularity.

Spacetime geometry of acoustics and electromagnetism

Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The resulting extensions are geometrically complete and phase-invariant (i.e., dual-symmetric) formulations that span all five grades of spacetime, with dynamical potentials and measurable fields spanning complementary grades that are related by a spacetime vector derivative (i.e., the quantum Dirac operator). These complete representations correct the equations of motion, energy–momentum tensors, forces experienced by probes, Lagrangian densities, and allowed gauge freedoms, while making manifest the deep structural connections to relativistic quantum field theories. Finally, we discuss the implications of these corrections to experimental tests.

On the absence of shock waves and vacuum birefringence in Born–Infeld electrodynamics

We study the interaction of two counter–propagating electromagnetic waves in vacuum in the Born–Infeld electrodynamics. First we investigate the Born case for linearly polarized beams, E · B = 0, i.e., G2=0 (crossed field configuration), which is identical for Born–Infeld and Born electrodynamics; subsequently we study the general Born–Infeld case for beams which are nonlinearly polarized, G2≠0. In both cases, we show that the nonlinear field equations decouple using self-similar solutions and investigate the shock wave formation. We show that the only nonlinear solutions are exceptional traveling wave solutions which propagate with constant speed and which do not turn into shocks for our approximation. We obtain two types of exceptional wave solutions, then we numerically analyze which phase velocities correspond to the counter- or co-propagating beams and subsequently we determine the direction of propagation of the exceptional waves.

Quantum effects of the conformal anomaly in a 2D model of gravitational collapse

The macroscopic effects of the quantum conformal anomaly are evaluated in a simplified two-dimensional model of gravitational collapse. The effective action and stress tensor of the anomaly can be expressed in a local quadratic form by the introduction of a scalar conformalon field φ, which satisfies a linear wave equation. A wide class of non-vacuum initial state conditions is generated by different solutions of this equation. An interesting subclass of solutions corresponds to initial states that give rise to an arbitrarily large semi-classical stress tensor leftlangle {T}_{mu}^{nu}rightrangle on the future horizon of the black hole formed in classical collapse. These lead to modification and suppression of Hawking radiation at late times after the collapse, and potentially large backreaction effects on the horizon scale due to the conformal anomaly. The probability of non-vacuum initial conditions large enough to produce these effects is estimated from the Gaussian vacuum wave functional of φ in the Schrödinger representation and shown to be mathcal{O} (1). These results indicate that quantum effects of the conformal anomaly in non-vacuum states are relevant for gravitational collapse in the effective theory of gravity in four dimensions as well.

Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves

We report on numerical simulations of critical phenomena near the threshold of black hole formation in the collapse of axisymmetric gravitational waves in vacuum. We discuss several new features of our numerical treatment, and then compare results obtained from families of quadrupolar and hexadecapolar initial data. Specifically, we construct (nonlinear) initial data from quadrupolar and hexadecapolar, time-symmetric wavelike solutions to the linearized Einstein equations (often referred to as Teukolsky waves), and evolve these using a shock-avoiding slicing condition. While our degree of fine-tuning to the onset of black-hole formation is rather modest, we identify several features of the threshold solutions formed for the two families. Both threshold solutions appear to display an at least approximate discrete self-similarity with an accumulation event at the center, and the characteristics of the threshold solution for the quadrupolar data are consistent with those found previously by other authors. The hexadecapolar threshold solution appears to be distinct from the quadrupolar one, providing further support to the notion that there is no universal critical solution for the collapse of vacuum gravitational waves.

Stability of Riemann solutions to a class of non-strictly hyperbolic systems of conservation laws

This paper is concerned with Riemann problem for a class of non-strictly hyperbolic systems of conservation laws. The two kinds of Riemann solutions including vacuum and delta shock wave are constructed. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of delta shock wave solutions. Furthermore, by studying the interactions among of the delta shock wave and vacuum as well as contact discontinuity, the Riemann solutions with four kinds of different structures are obtained. Additionally, the stability of the Riemann solutions is obtained under certain perturbation of the initial data.

Effective Hamiltonian for the system of the electromagnetic field and charged particles

A classical system of point charged particles and electromagnetic field is investigated in the general formulation, in which there is no direct interaction of the particles with each other. Particles are assumed to be non-relativistic for research simplicity. The point of view is defended that gauge choice determines the physical picture of processes in the system. The idea of extended gauge, in which scalar φk and longitudinal part Alnk of the vector potentials transform separately for large and small wave numbers, is proposed. Moreover, in the new gauge φk ≠ 0 only when k ≥ k0 and Alnk ≠ 0 only when k ≤ k0 , where k0 is a certain wave number. This greatly simplifies the study of the system dynamics, in which the transversecomponents Atnk of the vector potential are taken into account and do not change at the gauge transformation. Basing on the extended gauge idea, it is established that the system has a massive oscillatory mode described by a transverse potential Atnk and an oscillatory mod described by a longitudinal potential Alnk with the laws of dispersion (ωk2 + ω02 )1/2 і ω0, respectively (ωk = ck is the dispersion law for electromagnetic waves in vacuum, and ω0 is the plasma frequency). These modes can be called electromagnetic and plasma ones. At the same time, effective interaction between charged particles is introduced, which describes the screening effect. A connection of our work with Bohm and Pines investigations related to the presence of plasma modes in a Coulomb system, in which they do not use idea of gauge transformations, is analyzed.

Infrared Yang-Mills wave functional due to percolating center vortices

Inspired by the center-vortex dominance in the infrared sector of $SU(N)$ Yang-Mills theory observed on the lattice, we propose a vacuum wave functional localized on an ensemble of correlated center vortices endowed with stiffness and magnetic monopoles that change the orientation of the vortex flux. In the electric-field representation, this wave functional becomes an effective partition function for N complex scalar fields. The inclusion of both oriented and nonoriented vortices as well as so-called N-vortex matchings leads to an effective potential that has only a center symmetry left. In the center-vortex condensed phase, this symmetry is spontaneously broken. In this case, the Wilson loop average can be approximated by a solitonic saddle point localized around the minimal surface. The asymptotic string tension thus obtained displays Casimir scaling.

Gauge invariants of linearized gravity with a general background metric

In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants per se for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. If the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.

Nonlinear transient response of elastoplastic sandwich beam in underwater blast and the fluid-structure interaction

This work focuses on a new theory on the transient response of elastoplastic sandwich beam in underwater blast, and two fully coupled fluid-structure interaction (FSI) models are proposed, to gain insight into the propagation and dissipation of underwater blast wave, and the optimal design for sandwich structure with excellent underwater blast resistance. Based on the nonlinear dynamic high-order sandwich panel theory (EHSAPT) according to the authors’ preceding work [1], the governing equation of motion is constructed and modified by integrating the rarefaction-wave-related term into the structural damping matrix. So, the underwater blast analysis is transformed into the dynamic response of sandwich structure with structural damping under the superposition of incident and reflected waves in vacuum. Furthermore, this governing equation is simplified to get the analytical solution of impulse transferred to the sandwich structure, by implementing displacement and core rigidity assumptions. Finite element simulation and two existing FSI models are used to validate the accuracy. Conclusions are drawn that, the key aspects dominating FSI mechanism and time-domain response include pressure signatures, fluid characteristics, front-face mass, core density, and core elastic modulus, and the quantitative relationships are provided. Moreover, the core elastic modulus dominates the impulse transmitted to the sandwich structure, and the core strength and strain hardening govern the pressure delivered to the supports.

Logic proves that time does not get faster or slower (the universe is not produced by the singularity big bang)

I use the axiom that equal conditions must have the same result. Axiom proves that no matter how the velocity of an object changes, the time of all objects remains unchanged and unified. Time can be expressed as an eternal constant. Time belongs to the abstract concept of material attributes, and time is not a material concept. There is an abstract concept of uniform velocity in the universe (For example, the velocity of light wave in vacuum is constant “C”). According to the constant and uniform velocity of time, an important physical theory is proved: the universe is not produced by the singularity big bang. Mathematical classification code: 00A79;83F05;00A30;03A05;70A05;70F20;03A10;03F03.

Long-time behavior of a nonlinear electromagnetic wave in vacuum beyond the linear approximation

A quantum nature of vacuum is expected to affect electromagnetic fields in vacuum as a nonlinear correction, yielding nonlinear Maxwell's equations. We extend the finite-difference time-domain (FDTD) method in the case that the nonlinear electromagnetic Lagrangian is quartic with respect to the electric field and magnetic flux density. With this extension, the nonlinear Maxwell's equations can be numerically solved without making any assumptions on the electromagnetic field. We demonstrate examples of self-modulations of nonlinear electromagnetic waves in a one-dimensional cavity, in particular, in a timescale beyond an applicable range of linear approximation. A momentarily small nonlinear correction can accumulate and a comparably large self-modulation can be achieved in a long timescale even though the electromagnetic field is not extremely strong. Further, we analytically approximate the nonlinear electromagnetic waves in the cavity and clarify the characteristics, for example, how an external magnetic flux density changes the self-modulations of phase and polarization.

Light-cone distribution amplitudes of the nucleon and \u2206 baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Solving Maxwell's Equations for a Cylindrical Wave in Vacuum

Solving Maxwell's Equations for a Cylindrical Wave in Vacuum

Solving Maxwell's Equations for a Cylindrical Wave in Vacuum

Solving Maxwell's Equations for a Cylindrical Wave in Vacuum

Generation of high order harmonics in Heisenberg–Euler electrodynamics

High order harmonic generation by extremely intense, interacting, electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg–Euler formalism. Two intersecting plane waves of finite duration are considered in the case of general polarizations. Detailed finite expressions are obtained for the case where only the first Poincaré invariant does not vanish. Yields of high harmonics in this case are most effective.

Wave-driven torques to drive current and rotation

In the classic Landau damping initial value problem, where a planar electrostatic wave transfers energy and momentum to resonant electrons, a recoil reaction occurs in the nonresonant particles to ensure momentum conservation. To explain how net current can be driven in spite of this conservation, the literature often appeals to mechanisms that transfer this nonresonant recoil momentum to ions, which carry negligible current. However, this explanation does not allow the transport of net charge across magnetic field lines, precluding E × B rotation drive. Here, we show that in steady state, this picture of current drive is incomplete. Using a simple Fresnel model of the plasma, we show that for lower hybrid waves, the electromagnetic energy flux (Poynting vector) and momentum flux (Maxwell stress tensor) associated with the evanescent vacuum wave become the Minkowski energy flux and momentum flux in the plasma and are ultimately transferred to resonant particles. Thus, the torque delivered to the resonant particles is ultimately supplied by the electromagnetic torque from the antenna, allowing the nonresonant recoil response to vanish and rotation to be driven. We present a warm fluid model that explains how this momentum conservation works out locally, via a Reynolds stress that does not appear in the one-dimensional initial value problem. This model is the simplest that can capture both the nonresonant recoil reaction in the initial-value problem, and the absence of a nonresonant recoil in the steady-state boundary value problem, thus forbidding rotation drive in the former while allowing it in the latter.

Longitudinal electromagnetic waves with extremely short wavelength

Electromagnetic waves in vacuum and most materials have transverse polarization. Longitudinal electromagnetic waves with electric field parallel to wave vector are very rare and appear under special conditions in a limited class of media, for example in plasma. In this work, we study the dispersion properties of an easy-to-manufacture metamaterial consisting of two three-dimensional cubic lattices of connected metallic wires inserted one into another, also known as an interlaced wire medium. It is shown that the metamaterial supports longitudinal waves at extremely wide frequency band from very low frequencies up to the Bragg resonances of the structure. The waves feature unprecedentedly short wavelengths comparable to the period of the material. The revealed effects highlight spatially dispersive response of interlaced wire medium and provide a route toward generating electromagnetic fields with strong spatial variation.

Nonlinear waves in a dispersive vacuum described with a high order derivative electromagnetic Lagrangian

In this article we use an electromagnetic Lagrangian constructed so as to include dispersive effects in the description of an electromagnetic wave propagating in the quantum electrodynamic vacuum. This Lagrangian is Lorentz invariant, includes contributions up to six powers in the electromagnetic fields, and involves both fields and their first derivatives. Conceptual limitations inherent to the use of this higher derivative Lagrangian approach are discussed. We consider the one-dimensional spatial limit and obtain an exact solution of the nonlinear wave equation recovering the Korteveg-de Vries type periodic waves and solitons given in S. V. Bulanov et al. [Phys. Rev. D 101, 016016 (2020)].