Related papers: The Hilbert transform: Applications to atomic spec…
We consider reflection and transmission of interfaces which implement renormalisation group flows between conformal fixed points in two dimensions. Such an RG interface is constructed from the identity defect in the ultraviolet CFT by…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
We employ the Kramers-Henneberger Hamiltonian for time-independent calculations of multi-photon ionization of atoms with one and two electrons. As compared to the electromagnetic interaction in the length and velocity gauges, the presently…
In THz reflection spectroscopy the complex permittivity of an opaque medium is determined on the basis of the amplitude and of the phase of the reflected wave. There is usually a problem of phase error due to misplacement of the reference…
We consider the time delay of interfering single photons oppositely traveling in the Kerr metric of a rotating massive object. Classically, the time delay shows up as a phase difference between coherent sources of light. In quantum…
Light crossing dark domain walls that source a top form coupled to gauge Chern--Simons terms mixing visible and dark $U(1)$ gauge fields generically converts into dark photons. The effect is entirely localized on the wall and requires no…
In this paper, we analyze the nonlinear single pixel X-ray transform $K$ and study the reconstruction of $f$ from the measurement $Kf$. Different from the well-known X-ray transform, the transform $K$ is a nonlinear operator and uses a…
In this study, we introduce the first-of-its-kind class of tests for detecting change points in the distribution of a sequence of independent matrix-valued random variables. The tests are constructed using the weighted square integral…
We report enhanced transmission in measurements of the spectral dependence of forward light scattering by a high-density and cold ensemble of 87Rb atoms. This phenomenon, which is a result of dipole-dipole interaction induced cooperative…
We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while Gabor analysis is associated with unitary irreducible…
The goal of the paper is to obtain analogs of the sampling theorems and of the Riesz-Boas interpolation formulas which are relevant to the Discrete Hilbert and Kak-Hilbert transforms in $l^{2}$.
The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time…
We develop the theoretical tools necessary to promote electro-optic sampling to a time-domain quantum tomography technique. Our proposed framework implements detection of the time evolution of both the electric-field of a propagating…
In this paper we study some new properties of c-K-g-frames in a Hilbert space H. We study duals of c-K-g-frames and give some characterizations of c-K-g-frames and their duals. Also, we verify the relationships between c-K-g-frames and…
Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity, absorption, emission and scattering of radiation, charged particles stopping and…
This note focuses on recent results in spectral analysis of canonical systems of differential equations obtained via the approach developed in our previous papers \cite{MIF1, MP3, etudes, etudes2, PZ, Direct}. Many of our results are…
We propose an entanglement-enhanced sensing scheme that is robust against spatially inhomogeneous always-on Ising interactions. Our strategy is to tailor coherent quantum dynamics employing the Hilbert-space fragmentation (HSF), a recently…
We prove several theorems concerning the exceptional sets of Hilbert transform on the real line. In particular, it is proved that any null set is exceptional set for the Hibert transform of an indicator function. The paper also provides a…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
The paper introduces hidden grid background oriented schlieren for quantitative study and visualization of natural convection heat transfer. In this technique, the refractive index variation, induced by the temperature gradient, is encoded…