Related papers: A bound on group velocity for Bloch wave packets
The group velocity for pulses in an optical medium can be negative at frequencies between those of a pair of laser-pumped spectral lines. The gain medium then can amplify the leading edge of a pulse resulting in a time advance of the pulse…
We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction…
We study numerically the dynamics of a one-electron wave packet in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schr\"{o}dinger equation is…
General relativity predicts that gravitational waves propagate at the speed of light. Although ground-based gravitational-wave detectors have successfully constrained the velocity of gravitational waves in the high-frequency range,…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
Traveling wave solutions, in the form $u(x,t)=f(x+ct)$, to the generalized Burgers-Fisher equation $$ \partial_tu=u_{xx}+k(u^n)_x+u^p-u^q, \quad (x,t)\in\mathbb{R}\times(0,\infty), $$ with $n\geq2$, $p>q\geq1$ and $k>0$, are classified with…
We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The proof uses energy methods, which are adaptions of…
The group delay incurred by an optical wave packet depends on its path length. Therefore, when a wave packet is obliquely incident on a planar homogeneous slab, the group delay upon traversing it inevitably increases with the angle of…
Bloch's theorem was a major milestone that established the principle of bandgaps in crystals. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations for Bloch's theorem, this…
Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the…
We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.
We study super Bloch oscillations of ultracold atoms in a shaken lattice potential, subjected to a harmonically modulated mean-field interaction. Usually, any interaction leads to the decay of the wave packet and its super Bloch…
We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…
In this brief report, the group velocity of the eigen-modes in sonic crystals is derived, and shown to equal the averaged energy velocity of the eigen-modes. How the group velocity can be used to describe acoustic energy flows in sonic…
In situ particle acceleration is probably occuring in cluster radio haloes. This is suggested by the uniformity and extent of the haloes, given that spatial diffusion is slow and that radiative losses limit particle lifetimes. Stochastic…
We ask the question 'what happens to Bloch waves in gratings synthetically moving at near the speed of light?'. First we define a constant refractive index (CRI) model in which Bloch waves remain well defined as they break the light…
Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…
Recently, Bohmian mechanics has been challenged [Nature 643, 67 (2025)] by studying a system in which the motion of particles cannot be associated only with the gradient of phase of the wave function. We point out that, in general, Bohmian…
We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice…