Related papers: Spectra of absolute instruments from the WKB appro…
We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed,…
This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…
We propose a class of magnifying absolute optical instruments with a positive isotropic refractive index. They create magnified stigmatic images, either virtual or real, of optically homogeneous three-dimensional spatial regions within…
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M + g q^N)$, where $N>M>0$ even, and…
We developed a novel technique for frequency measurement and synthesis, based on the operation of a femtosecond comb generator as transfer oscillator. The technique can be used to measure frequency ratios of any optical signals throughout…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
Available laser technology is opening the possibility of testing QED experimentally in the so-called strong-field regime. This calls for developing theoretical tools to investigate strong-field QED processes in electromagnetic fields of…
We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few different techniques are employed: the most sophisticated, which relates the 1-skeleton of the polytope to a Cayley graph, is based on methods akin to…
A novel and simple approach to optical wavelength measurement is presented in this paper. The working principle is demonstrated using a tunable waveguide micro ring resonator and single photodiode. The initial calibration is done with a set…
Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter epsilon and…
We compute the quasi-bound state spectra of ultralight scalar and vector fields around rotating black holes. These spectra are determined by the gravitational fine structure constant $\alpha$, which is the ratio of the size of the black…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
The spectrogram is a classical DSP tool used to view signals in both time and frequency. Unfortunately, the Heisenberg Uncertainty Principal limits our ability to use them for detecting and measuring narrowband signal modulation in wideband…
The complex eigenfrequencies of a perfectly conducting cone, truncated cone, and finite circular cylinder are determined using the time-domain integral equation method and the Prony technique.
Optical clocks with unprecedented accuracy of 10^(-18) will lead to innovations in many research areas. All the applications of optical clocks rely on the ability of precisely converting the frequency from one optical clock to another, or…
Electron-beam microscopy and spectroscopy featuring atomic-scale spatial resolution have become essential tools used daily in almost all branches of nanoscale science and technology. As a natural supercontinuum source of light, free…
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…
This paper studies sensor calibration in spectral estimation where the true frequencies are located on a continuous domain. We consider a uniform array of sensors that collects measurements whose spectrum is composed of a finite number of…
This is a survey of approximate cloaking using transformation optics for acoustic and electromagnetic waves.
By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these…