Related papers: Interpolation between para-Bose and para-Fermi sta…
The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimension. In principle, a second exception known as parastatistics, which…
In interferometers, the more information about the quanta's path available in an ancillary quantum system (AQS), the less visibility the interference has. By use of Shannon entropy, we try to compare the amount of which-phase information…
This is a study of $q$-Fermions arising from a q-deformed algebra of harmonic oscillators. Two distinct algebras will be investigated. Employing the first algebra, the Fock states are constructed for the generalized Fermions obeying Pauli…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
Roughly speaking, a near-best (abbr. NB) quasi-interpolant (abbr. QI) is an approximation operator of the form $Q_af=\sum_{\alpha\in A} \Lambda_\alpha (f) B_\alpha$ where the $B_\alpha$'s are B-splines and the $\Lambda_\alpha (f)$'s are…
The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and…
We give a description, in analytic and geometric terms, of the interpolation sequences for the algebra of entire functions of exponential type which are bounded on the real line.
In quantum interferometry, it is vital to control and utilize nonlinear interactions for achieving high-precision measurements. Attribute to their long coherent time and high controllability, ultracold atoms including Bose condensed atoms…
We consider the small, of the size of the order of the wavelength, interferometer with the main mode excited by a quantum field from a nano-LED or a laser. The input field is detuned from the interferometer mode with, on average, a few…
We combine continuous $q^{-1}$-Hermite Askey polynomials with new $2D$ orthogonal polynomials introduced by Ismail and Zhang as $q$-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative…
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…
Bosonic and fermionic statistics are well known to give rise to antinomic behaviors, most notably boson bunching vs fermion antibunching. Here, we establish a fundamental relation that combines bosonic and fermionic multiparticle…
The aim of this paper is to study the approximation of functions using a higher order Hermite-Fejer interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit…
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of…
We construct the fluctuation algebra for fermions in a quasifree state and its timedependence for quasifree evolutions. We find a Bose-Einstein-condensate and study its stability under interaction.
We consider a system of one-dimensional non-interacting fermions in external harmonic confinement. Using an efficient Green's function method we evaluate the exact profiles and the pair correlation function, showing a direct signature of…
General results of interpolation (eg. Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebra $F^\infty$ (resp. noncommutative disc algebra $A_n$) with consequences to the interpolation by bounded operator-valued…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…