Related papers: Wave manipulation via delay-engineered periodic po…
In this work, we study the stabilization of the wave equation using an internal delayed potential. Interestingly, the stabilization mechanism is entirely induced by the delay, since exponential stabilization cannot be achieved in its…
We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave…
A toroidal trap combined with external time-dependent electric field can be used for implementing different dynamical regimes of matter waves. In particular, we show that dynamical and stochastic acceleration, localization and…
We theoretically investigate the homogenization of the dielectric response to transverse electric waves of a transverse grating characterized by the Kapitza condition, i.e. the permittivity is rapidly modulated with a modulation depth…
The advent of novel nonlinear materials has stirred unprecedented interest in exploring the use of temporal inhomogeneities to achieve novel forms of wave control, amidst the greater vision of engineering metamaterials across both space and…
We report on the experimental realization of a Kapitza pendulum for ultracold atoms. Using time-periodic attractive and repulsive Gaussian potentials, we create an effective trap for ultracold neutral atoms in a regime where the time…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
A pulse of matter waves may dramatically change its shape when traversing an absorbing barrier with time-dependent transparency. Here we show that this effect can be utilized for controlled manipulation of spatially-localized quantum…
In order to confine waves beyond the diffraction limit, advances in fabrication techniques have enabled subwavelength structuring of matter, achieving near-field control of light and other types of waves. The price is often expensive…
Electromagnetic temporal boundaries, emerging when the constitutive parameters of a medium undergo abrupt temporal variations, have garnered significant interest for their role in facilitating unconventional wave phenomena and enabling…
Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description the effect is time-independent. In the…
The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in…
When propagating through periodically structured media, i. e. photonic crystals, optical waves will be modulated with the periodicity. As a result, the dispersion of waves will no longer behave as in a free space, and so called frequency…
The quantum states of the Kapitza pendulum are described within the effective potential obtained by the method of averaging over the fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using…
We introduce a Kapitza-like mechanism for the near-field radiative heat transfer and show that fast modulation of any parameter controlling the flux, such as the vacuum gap or a material response, produces a quadratic, time-averaged…
Recently, many evidences demonstrate that partial Differential Phase Shift Keying (i.e., when the delay inside the Delay Interferometer is shorter than the symbol period) can partially compensate the signal deformation caused by spectrally…
A discrete analogue of the dynamical (Kapitza) trapping effect, known for classical and quantum particles in rapidly oscillating potentials, is proposed for light waves in modulated graded-index waveguide lattices. As in the non-modulated…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory…