相关论文: Uncertainty principles for orthonormal bases
The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy.…
This paper focuses on the complex relationship between Heisenberg's Uncertainty Principle and the nodal structure of wave functions in a variety of quantum systems including the quantum harmonic oscillator, the particle in a 1D box , and…
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 study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable…
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…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory…
To more flexibly balance between exploration and exploitation, a new meta-heuristic method based on Uncertainty Principle concepts is proposed in this paper. UP is is proved effective in multiple branches of science. In the branch of…
By building on our earlier work, we establish uncertainty principles in terms of Heisenberg inequalities and of the ambiguity functions associated with magnetic structures on certain coadjoint orbits of infinite-dimensional Lie groups.…
Given a frame in C^n which satisfies a form of the uncertainty principle (as introduced by Candes and Tao), it is shown how to quickly convert the frame representation of every vector into a more robust Kashin's representation whose…
The aim of this paper is to prove a logarithmic and a Hirschman-Beckner entropic uncertainty principles for the Hankel wavelet transform. Then we derive a general form of Heisenberg-type uncertainty inequality for this transformation.
In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of…
In this paper we look at a particular realization of Popper's thought experiment with correlated quantum particles and argue that, from the point of view of a nonlinear quantum physics and contrary to the orthodox interpretation,…
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.
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
Uncertainty relation for photons that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in…
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…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
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)…
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of…