Related papers: Uncertainty relations and applications in spectral…
The properties of two forms of the gradient expanded Kadanoff--Baym equations, i.e. the Kadanoff--Baym and Botermans-Malfliet forms, suitable to describe the transport dynamics of particles and resonances with broad spectral widths, are…
We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to…
Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the…
This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular measures, especially the case of OPRL and OPUC. Links…
These are extended lecture notes for a mini course at the Spring School on Non-Archimedean Geometry and Eigenvarieties held at Heidelberg University in March 2023. The goal of the course is to explain a modern take on the eigenvariety…
We introduce occupation uncertainty relations (OURs) for dynamics of a Markov process over discrete configurations. Those are lower bounds on uncertainties of system observables that are time-integrated along stochastic trajectories. The…
Talk at the 25th Johns Hopkins Workshop "2001: A Relativistic Spacetime Odyssey", Firenze September 2001.
This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective…
We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of…
A concise derivation of all uncertainty relations is given entirely within the context of phase-space quantization, without recourse to operator methods, to the direct use of Weyl's correspondence, or to marginal distributions of x and p.
This contribution contains a summary of the Krakow meeting on Soft Physics and Fluctuations. It emphasizes both the experimental and the theoretical investigations on correlations/fluctuations and intermittency in multi-particle processes…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory with a digression on Riesz bases. The second and third…
We address the problem of learning reusable state representations from streaming high-dimensional observations. This is important for areas like Reinforcement Learning (RL), which yields non-stationary data distributions during training. We…
Derivation of $\kappa$-Poincare bicovariant commutation relations between coordinates and 1-forms on $\kappa$-Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U(1) gauge theory and appearance of an…