Related papers: On the Uncertainty Principle for Metaplectic Trans…
We introduce a notion of localization for dyadic functions, i.e. functions defined on the Cantor group. Localization is characterized by functional $UC_d$ similar to the Heisenberg uncertainty constant used for real-line functions. We are…
It is shown how the uncertainty principle can provide a mechanism for the generation of fluctuations of very diverse scales in the early universe. This phenomenon could account for the large-scale structure observed today.
In this paper we consider uncertainty principles for solutions of certain PDEs on H-type groups. We first prove that, contrary to the euclidean setting, the heat kernel on H-type groups is not characterized as the only solution of the heat…
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute…
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…
Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg…
As a time-shifted and frequency-modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and…
We extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this extension to show that Hardy's uncertainty principle is…
Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.
In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have…
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.
In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…
A general approach to transference principles for discrete and continuous operator (semi)groups is described. This allows to recover the classical transference results of Calder\'on, Coifman and Weiss and of Berkson, Gillespie and Muhly and…
The String Uncertainty Relations have been known for some time as the stringy corrections to the original Heisenberg's Uncertainty principle. In this letter the Stringy Uncertainty relations, and corrections thereof, are explicitly derived…
Heisenberg introduced his famous uncertainty relations in a seminal 1927 paper entitled "The Physical Content of Quantum Kinematics and Mechanics". He motivated his arguments with a gedanken experiment, a gamma ray microscope to measure the…
We show that a well known uncertainty principle for functions on the circle can be derived from an uncertainty principle for the Euclidean motion group.
The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation,…
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…