Related papers: On uncertainty principles in the finite dimensiona…
The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called…
These lecture notes are devoted to selected topics related to the uncertainty principle in harmonic analysis. Rather than attempting a systematic treatment, we emphasize only a number of both classical and deep manifestations of this…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
Given two orthornormal bases A and B, the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring A and B onto a given quantum state. State independent lower…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
Motivated by recent works, we employ the bounds on the dimensionless quantum-gravity parameter obtained from six gravitational tests in order to obtain bounds on the dimensionless parameter of the generalized uncertainty principle with…
A generalized uncertainty principle is obtained from a conformally transformed action containing a scalar field and a unique constraint. The constraint's Lagrange multiplier is found to obey a relativistic diffusion equation transforming…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a discrete random polymer measure, as well as a universality…
We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner…
Multimodal foundation models offer promising advancements for enhancing driving perception systems, but their high computational and financial costs pose challenges. We develop a method that leverages foundation models to refine predictions…
Fiber orientation is decisive for the mechanical performance of composite materials. During manufacturing, variations in material and process parameters can influence fiber orientation. We employ multilevel polynomial surrogates to model…
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
A version of the Uncertainty Principle says: There does not exist a non zero function in $L_p(\mathbb{R}^d)$ if its Fourier transform is supported by a set of finite $\alpha$-Hausdorff measure with $\alpha<2d/p$. This UP does not hold at…
The main objective of the present paper is to establish a new uncertainty principle (UP) for the two-sided quaternion Fourier transform (QFT). This result is an extension of a result of Benedicks, Amrein and Berthier, which states that a…
Heisenberg and Schr{\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$, in a state $\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not…
The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty…