Related papers: Spectra of absolute instruments from the WKB appro…
The method of the optical approximation is used to estimate the high frequency impedances of different vacuum chamber transitions of the European XFEL beam line. The approximations of the longitudinal impedances are obtained in terms of…
It is well known that the standard projection methods allow one to recover the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to spurious eigenvalues lying in the gaps of the essential…
Particulate materials include powders, emulsions, composites, and many others. This is why measuring these has become important for both industry and scientific applications. For industrial applications, the greatest need is to measure…
The electronic response of a telescope under direct illumination by a point-like light source is based on photon counting. With the data obtained using the SNDICE light source and the Megacam camera on the CFHT telescope, we show that the…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
We analyse the accuracy of the approximate WKB quantization for the case of general one-dimensional quartic potential. In particular, we are interested in the validity of semiclassically predicted energy eigenvalues when approaching the…
We present a method for the in-flight relative flux self-calibration of a spectro-photometer instrument, general enough to be applied to any upcoming galaxy survey on satellite. The instrument response function, that accounts for a smooth…
Fast and accurate computations of the power spectrum of cosmic microwave background fluctuations are essential for comparing current and upcoming data sets with the large parameter space of viable cosmological models. The most efficient…
We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that…
I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…
It is shown that a highly equidistant optical frequency comb can be generated by the parametric excitation of an optical bottle microresonator with nanoscale effective radius variation by its natural mechanical vibrations.
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
We present design and realization of an ultra-broadband optical spectrometer capable of measuring the spectral intensity of multi-octave-spanning light sources on a single-pulse basis with a dynamic range of up to 8 orders of magnitude. The…
A new algorithm for computing the accurate values of quasinormal frequencies of extremal Reissner-Nordstr\"{o}m black holes is presented. The numerically computed values are consistent with the values earlier obtained by Leaver and those…
Numerical relativity simulations provide a full description of the dynamics of binary systems, including gravitational radiation. The waveforms produced by these simulations have a number of applications in gravitational-wave detection and…
For 2D periodic Jacobi operators we obtain the estimate of the Lebesgue measure of the spectrum and estimates of edges of spectral bands.
In recent years, a great deal of emphasis has been placed on achieving the diffraction limit with large aperture telescopes. For a well matched focal-plane instrument, the diffraction limit provides the highest possible angular resolution…
An exact WKB treatment of 1-d homogeneous Schr\"odinger operators (with the confining potentials $q^N$, $N$ even) is extended to odd degrees $N$. The resulting formalism is first illustrated theoretically and numerically upon the spectrum…
We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our…