Related papers: Wigner measures in the discrete setting: high-freq…
Let $Q(x)$ denote a periodic function on the real line. The Schr\"odinger operator, $H_Q=-\partial_x^2+Q(x)$, has $L^2(\mathbb{R})-$ spectrum equal to the union of closed real intervals separated by open spectral gaps. In this article we…
Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of random vectors, namely probability measures or more simply…
Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…
Periodic activation functions, often referred to as learned Fourier features have been widely demonstrated to improve sample efficiency and stability in a variety of deep RL algorithms. Potentially incompatible hypotheses have been made…
The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body…
We present the experimental reconstruction of the Wigner function of an individual electronic spin qubit associated with a nitrogen-vacancy (NV) center in diamond at room temperature. This spherical Wigner function contains the same…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…
Self-consistent computations of the potential profile in complex semiconductor heterostructures can be successfully applied for comprehensive simulation of the gain and the absorption spectra, for the analysis of the capture, escape,…
We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation \emph{Short-time Fourier Transform} (STFT) is replaced by the $\mathcal{A}$-\emph{Wigner distribution} defined by $W_{\mathcal A}…
We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calder\'on-Zygmund operators in harmonic…
The Wigner time delay of slow particles in the process of their elastic scattering by complex targets formed by several zero-range potentials is investigated. It is shown that at asymptotically large distances from the target, the…
The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form…
Consistent reconstruction is a method for producing an estimate $\widetilde{x} \in \mathbb{R}^d$ of a signal $x\in \mathbb{R}^d$ if one is given a collection of $N$ noisy linear measurements $q_n = \langle x, \varphi_n \rangle +…
Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known as highly relevant, in…
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum…