Related papers: Transient amplification in stable Floquet media
Time-dependent fluid dynamics plays a crucial role in both natural phenomena and industrial applications. Understanding the flow instabilities and transitions within these dynamical systems is essential for predicting and controlling their…
We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see…
An electromagnetic wave-packet propagating in a linear, homogeneous, and isotropic medium changes shape while its envelope travels with different velocities at different points in spacetime. In general, a wave-packet can be described as a…
We consider a degenerate abstract wave equation with a time-dependent propagation speed. We investigate the influence of a strong dissipation, namely a friction term that depends on a power of the elastic operator. We discover a threshold…
We perform a theoretical investigation into the classical and quantum dynamics of an optical field in a cavity containing a moving membrane ("membrane-in-the-middle" set-up). Our approach is based on the Maxwell wave equation, and…
This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
Four-dimensional optics leverages the simultaneous control of materials in space and time to manipulate light. A key challenge in experimentally realizing many intriguing phenomena is the need for rapid modulation, which is hindered by the…
The non-modal approach for a linearized system differs from a normal mode analysis by following the temporal evolution of some perturbed equilibria, and therefore includes transient effects. We employ a non-modal approach for studying the…
Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual…
We develop a model for parametric amplification, based on a density matrix approach, which naturally accounts for the peculiarities arising for matter waves: significant depletion and explicit time-dependence of the source state population,…
We study the implications of time-varying wave mechanics, and show how the standard wave equation is modified if the speed of a wave is not constant in time. In particular, waves which experience longitudinal acceleration are shown to have…
We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy)…
Optical instabilities in moving media are linked to a spontaneous parity-time symmetry breaking of the system. It is shown that in general the time evolution of the electromagnetic waves in moving media is determined by a non-Hermitian…
In this study, we experimentally investigate the application of a transient signal with complex frequencies to the absorption and transmission of sound waves. Indeed, the emission of a wave with an exponentially varying amplitude in time is…
A light beam normally incident upon an uniformly moving dielectric medium is in general subject to bendings due to a transverse Fresnel-Fizeau light drag effect. In conventional dielectrics, the magnitude of this bending effect is very…
Theory of the optical parametric amplification at high-frequency pumping in crystals with a regular space modulation of the sign of nonlinear coupling coefficient of interacting waves is developed. By applying the matrix method, the theory…
Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the…
Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…