Related papers: Some Arguments for the Wave Equation in Quantum Th…
We clarify some arguments concerning Jefimenko's equations, as a way of constructing solutions to Maxwell's equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial…
The notion of ``radiating'' and ``non-radiating'' current sources in classical electrodynamics plays an important role in calculations of direct and inverse electromagnetic scattering problems. Such a decomposition of the current is central…
We study the decay process of an unstable quantum system, especially the deviation from the exponential decay law. We show that the exponential period no longer exists in the case of the s-wave decay with small $Q$ value, where the $Q$…
A connection between classical non-radiating sources and free-particle wave equations in quantum mechanics is rigorously made. It is proven that free-particle wave equations for all spins have currents which can be defined which are…
We prove there exists a charge solution to the 1-dimensional wave equation, and a corresponding current, such that the pair satisfy the continuity equation. We show that when they are extended to a smooth solution of the continuity equation…
A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this…
We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. We show that if the damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the boundary…
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…
We consider finite-energy solutions to the defocusing nonlinear wave equation in two dimensional space. We prove that almost all energy moves to the infinity at almost the light speed as time tends to infinity. In addition, the…
By controlling coefficients and decaying order of time-decaying harmonic potentials, the velocity of a quantum particle is decelerated by the effect of harmonic potentials but the particle is non-trapping. In this paper, we consider the…
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of…
We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null condition appear in many equations in…
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used.…
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…
We prove a unique continuation from infinity theorem for regular waves of the form $[ \Box + \mathcal{V} (t, x) ]\phi=0$. Under the assumption of no incoming and no outgoing radiation on specific halves of past and future null infinities,…
We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…
To understand an oft-observed but poorly understood phenomenon in which a solitary wave in a dispersive equation slowly deteriorates due to a persistent emission of radiation (i.e. a ``radiating solitary wave''), we propose a bare-bones…
In the first part of the present work, the correction to photon emission rate of an oscillating two-level atom in the presence of electromagnetic quantum vacuum field has been investigated for two different configurations: (i) Atom is…
We consider the radiative decay of atoms scattered by a resonant standing light wave. Scattering is shown to suppress the Rabi oscillations and to slow down the atomic radiative decay giving rise to a power law behavior of the…