Related papers: An uncertainty principle related to the Euclidean …
The windowed offset linear canonical transform (WOLCT) can be identified as a generalization of the windowed linear canonical transform (WLCT). In this paper, we generalize several different uncertainty principles for the WOLCT, including…
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…
Generalizations of coordinate $x$-momentum $p_x$ Uncertainty Principle, with $\Delta x$ and $\Delta p_x$ dependent terms ($\Delta$ denoting standard deviation), $$\Delta x \Delta p_x\geq i\hbar (1+\alpha\Delta p_x^2 +\beta \Delta x^2)$$…
Classical and recent results on uncertainty principles for functions on finite Abelian groups relate the cardinality of the support of a function to the cardinality of the support of its Fourier transforms. We use these results and their…
The Euclidean formulation of quantum gravity can be interpreted in terms of a probability distribution over Riemannian manifolds. In the context of de Sitter gravity, the statistics of the total volume according to this distribution is…
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…
Classical inequalities used in information theory such as those of de Bruijn, Fisher, and Kullback carry over from the setting of probability theory on Euclidean space to that of unimodular Lie groups. These are groups that posses…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
A universal theory of linear instabilities in swirling flows, occurring in both natural settings and industrial applications, is formulated. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
In this paper, we define Euclidean minima for function fields and give some bound for this invariant. We furthermore show that the results are analogous to those obtained in the number field case.
The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of the original proofs by Hardy, refers to the…
After a short introduction to the generalized uncertainty principle (GUP), we review some of the physical predictions of the GUP, and we focus in particular on the bounds that present experimental tests can put on the value of the…
Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the…
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
We show that Hardy's uncertainty principle can be reformulated in such a way that it has an analogue even for compact Lie groups and symmetric spaces of compact type.