Related papers: Uncertainty principles for the windowed Opdam--Che…
In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We first discuss that there should be a correction factor to the Heisenberg uncertainty principle (HUP) when torsional effects…
The goal of this paper is to combine ideas from the theory of mixed spectral problems for differential operators with new results in the area of the Uncertainty Principle in Harmonic Analysis (UP). Using recent solutions of Gap and Type…
Generalized uncertainty principles are effective changes to the Heisenberg uncertainty principle that emerge in several quantum gravity models. In the present letter, we study the consequences that two classes of these modifications yield…
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…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…
We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that…
A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic…
Dependency on the preparation of state for the Heisenberg uncertainty principle can be removed with the help of entropy uncertainty principle. The shortness of the uncertainty principle (UP) can be overcome with the help of the concept of…
In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be…
In this short paper a new thought experiment has been introduced to illustrate the famous Heisenberg's uncertainty principle based on Otto-Wiener's experiment (1890) associated with standing light waves. This illustration is quite easy as…
We discuss the Generalized Uncertainty Principle and the Extended Uncertainty Principle in the context of black hole solutions coming from non-local theories of gravity, focusing, specifically, on Infinite Derivative Gravity. We argue that…
In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated…
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…
A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of…