Related papers: Phase space localization of antisymmetric function…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
Motivated by Dynamic Mode Decomposition algorithms, we provide lower bounds on the dimension of a finite-dimensional subspace $F \subseteq \mathrm{L}^2(\mathrm{X})$ required for predicting the behavior of dynamical systems over long time…
Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum…
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
The coordinate-space wave function $\psi(x)$ of quasi-one-dimensional atoms is defined in the $x\geq 0$ region only. This poses a typical problem to write a physically acceptable momentum-space wave function $\phi(p)$ from the Fourier…
Phase difference function is established by means of phase transfer function between time domains of source and interference point. The function reveals a necessary interrelation between outcome of two-beam interference, source's frequency…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
If two signals are phase synchronous then the respective Fourier component at each spectral band should exhibit certain properties. In a pair of artificially generated phase synchronous signals the phase difference at each frequency band…
Optical entropy bounds for metal nanoparticles immersed in nonlinear optical media and for nonlinear dielectric microdroplets on metal surfaces are calculated near the frequency of the surface plasmon resonance. Similar to the…
We generalize the position- and momentum-space entanglement cuts to a family of cuts corresponding to regions in the classical phase space. We explicitly compute the entanglement spectra of free fermionic many-body wavefunctions for a…
The phase space structure of certain quantum states reveals structure on a scale that is small compared to the Planck area. Using an analog between the wavefunction of a single photon and the electric field of a classical ultrashort optical…
Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
We extend an estimate of Taibleson and Weiss, regarding Fourier transform of Hardy spaces, to the aniostropic setting. As consequences, we obtain necessary conditions for multiplier operators, and the anisotropic version of the…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…