Related papers: Generalized uncertainty principles
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…
Nonlocality is a distinctive feature of quantum theory, which has been extensively studied for decades. It is found that the uncertainty principle determines the nonlocality of quantum mechanics. Here we show that various degrees of…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.
We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including…
The Weinstein operator has several applications in pure and applied Mathematics especially in Fluid Mechanics and satisfies some uncertainty principles similar to the Euclidean Fourier transform. The aim of this paper is establish a…
The fundamental physical description of the Universe is based on two theories: Quantum Mechanics and General Relativity. Unified theory of Quantum Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG effects in…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the…
We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore…
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…
Let $G$ be a locally compact abelian group, and let $\widehat{G}$ denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any $S \subset G$ and $\Sigma \subset \widehat{G}$, there exists a…
It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
The uncertainty principle constitutes one of the famous physical concepts which continues to attract researchers from different related fields since its discovery due to its utility in many applications. Among the classical (Fourier-based)…
Various models of quantum gravity imply the Planck-scale modifications of Heisenberg's uncertainty principle into a so-called generalized uncertainty principle (GUP). The GUP effects on high-energy physics, cosmology, and astrophysics have…
From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
The present work proposes an alternative approach to the problem of the emergence of classicality. Typical approaches developed in the literature derive the classical behaviour of a quantum system from conditions that concern the value of…