Search results for "WAVE-EQUATION"
showing 4 items of 4 documents
Recovery of time-dependent coefficients from boundary data for hyperbolic equations
2019
We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.
Numerical study of the Kerr solution in rotating coordinates
2016
International audience; The Kerr solution in coordinates corotating with the horizon is studied as a testbed for a spacetime with a helical Killing vector in the Ernst picture. The solution is numerically constructed by solving the Ernst equation with a spectral method and a Newton iteration. We discuss convergence of the iteration for several initial iterates and different values of the Kerr parameters.
Coherent control of stimulated emission inside one-dimensional Photonic Crystals
2005
In this paper, the quasinormal mode (QNM) theory is applied to discuss the quantum problem of an atom embedded inside a one-dimensional (1D) photonic band gap (PBG) cavity pumped by two counterpropagating laser beams. The e.m. field is quantized in terms of the QNMs in the 1D PBG and the atom modeled as a two-level system is assumed to be weakly coupled to just one of the QNMs. The main result of the paper is that the decay time depends on the position of the dipole inside the cavity, and can be controlled by the phase difference of the two laser beams. © 2005 The American Physical Society
Quantum counter-propagation in open optical cavities via the quasi-normal-mode approach
2006
By using the quasi-normal-mode (QNM) formalism in a second quantization scheme, the problem of the counter-propagation of electromagnetic fields inside optical cavities is studied. The links between QNM operators and canonical destruction and creation operators describing the external free field, as well as the field correlation functions, are found and discussed. An application of the theory is performed for open cavities whose refractive index satisfies symmetric properties.