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Related papers: Sharp second order uncertainty principles

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This is the second part of study on the optimal convergence rate of the explicit Euler discretization in time for the convection-diffusion equations [Appl. Math. Lett. \textbf{131} (2022) 108048] which focuses on high-dimensional…

Numerical Analysis · Mathematics 2022-05-13 Qifeng Zhang , Jiyuan Zhang , Zhi-zhong Sun

The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…

Quantum Physics · Physics 2015-06-05 Iwo Bialynicki-Birula , Zofia Bialynicka-Birula

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…

Spectral Theory · Mathematics 2017-12-29 Nikolai Makarov , Alexei Poltoratski

In this paper, we obtain the optimal instability threshold of the Couette flow for Navier-Stokes equations with small viscosity $\nu>0$, when the perturbations are in the critical spaces $H^1_xL_y^2$. More precisely, we introduce a new…

Analysis of PDEs · Mathematics 2024-04-30 Hui Li , Nader Masmoudi , Weiren Zhao

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated…

Quantum Physics · Physics 2009-11-07 Masanao Ozawa

We explore the Hyers-Ulam stability of perturbations for a homogeneous linear differential system with $2\times 2$ constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers-Ulam stable are…

Classical Analysis and ODEs · Mathematics 2022-03-25 Douglas R. Anderson , Masakazu Onitsuka

For a Hamiltonian $H \in C^2(\mathbb{R}^{N \times n})$ and a map $u:\Omega \subseteq \mathbb{R}^n /!\longrightarrow \mathbb{R}^N$, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,\Omega) \ :=\…

Analysis of PDEs · Mathematics 2014-04-16 Nikos Katzourakis

The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…

Quantum Physics · Physics 2021-03-31 Xiao-Ming Lu , Xiaoguang Wang

This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…

Quantum Physics · Physics 2018-07-31 C. Huang , Yong-Chang Huang

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…

General Relativity and Quantum Cosmology · Physics 2017-04-18 Dongfeng Gao , Jin Wang , Mingsheng Zhan

Solutions to $p$-Laplace equations are not, in general, of class $C^2$. The study of Sobolev regularity of the second derivatives is, therefore, a crucial issue. An important contribution by Cianchi and Maz'ya shows that, if the source term…

Analysis of PDEs · Mathematics 2023-05-26 Luigi Montoro , Luigi Muglia , Berardino Sciunzi

We test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is…

General Relativity and Quantum Cosmology · Physics 2022-03-29 Fabrizio Tamburini , Fabiano Feleppa , Bo Thidé

When studying the weighted Hardy-Rellich inequality in $L^2$ with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in the first situation. Our contribution is to determine the new…

Analysis of PDEs · Mathematics 2024-06-25 Cristian Cazacu , Irina Fidel

The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…

Quantum Physics · Physics 2018-03-29 Yu-Xiang Zhang , Shengjun Wu , Zeng-Bing Chen

We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among…

Quantum Physics · Physics 2013-06-28 Marcelo A. Marchiolli , Paulo E. M. F. Mendonca

We provide a proof of strong maximum and minimum principles for fully nonlinear uniformly parabolic equations of second order. The approach is of parabolic nature, slightly differs from the earlier one proposed by L. Nirenberg and does not…

Analysis of PDEs · Mathematics 2023-07-25 Alessandro Goffi

We improve the constant $\frac{\pi}{2}$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi}{2}}$. For Hamming cube the sharp constant is not known,…

Probability · Mathematics 2019-06-04 Paata Ivanisvili , Dong Li , Ramon van Handel , Alexander Volberg

The Heisenberg position-momentum uncertainty principle shares with the equivalence principle the role of main pillar of our current description of nature. However, in its original formulation it is inconsistent with special relativity, and…

High Energy Physics - Theory · Physics 2022-09-12 Giovanni Amelino-Camelia , Valerio Astuti

Heisenberg's uncertainty principle states that it is not possible to compute both the position and momentum of an electron with absolute certainty. However, this computational limitation, which is central to quantum mechanics, has no…

Computational Complexity · Computer Science 2008-11-10 Stefan Jaeger

The model of kappa-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper we present new results concerning different sets of derivatives on the coordinate algebra of…

High Energy Physics - Theory · Physics 2009-11-10 Marija Dimitrijevic , Lutz Möller , Efrossini Tsouchnika