Related papers: The radiation field is a Fourier integral operator
Superradiant scattering is a radiation enhancement process that takes place in many contexts, and which has recently found exciting applications in astro and particle physics. In the framework of curved spacetime physics, it has been…
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source.…
A number of physical processes occurring in a flat one-dimensional graphene structure under the action of strong time-dependent electric fields are considered. It is assumed that the Dirac model can be applied to the graphene as a subsystem…
In signal processing, a signal is a function. Conceptually, replacing a function by its graph, and extending this approach to a more abstract setting, we define a signal as a submanifold M of a Riemannian manifold (with corners) that…
In this PhD Thesis we investigate the geometry of random fields on compact Riemannian manifolds, in particular the two-dimensional sphere. In the first part, we characterize isotropic Gaussian fields on homogeneous spaces of a compact group…
Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier…
We construct an effective Hamiltonian of interacting bosons, based on scattered radiation off vibrational modes of designed molecular architectures. Making use of the infinite yet countable set of spatial modes representing the scattering…
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier…
We develop a unified approach to the construction of the hyperbolic and elliptic Eisenstein series on a finite volume hyperbolic Riemann surface. Specifically, we derive expressions for the hyperbolic and elliptic Eisenstein series as…
We consider the continuous Anderson operator $H=\Delta+\xi$ on a two dimensional closed Riemannian manifold $\mathcal{S}$. We provide a short self-contained functional analysis construction of the operator as an unbounded operator on…
We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schroedinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields…
We establish various results on the large level limit of projective quantum representations of surface mapping class groups obtained by quantizing moduli spaces of flat SU(n)-bundle. Working with the metaplectic correction, we proved that…
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral…
The scattering of electromagnetic pulses is described using a non-singular boundary integral method to solve directly for the field components in the frequency domain, and Fourier transform is then used to obtain the complete space-time…
In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the…
In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy…
The quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, the Hamiltonian of the system is realized as a linear operator on a boson Fock space. It is proven…
We study the semi-classical behavior of the spectral function of the Schr\"{o}dinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward…
The aurora often breaks down into elongated filaments that are aligned with the geomagnetic field. It is natural to infer from this that when important structures are found in the electrostatic fields they, too, will follow a cylindrical…
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…