Related papers: Uncertainty principles for the Opdam-Cherednik tra…
In this paper, Morgan type uncertainty principle and unique continuation properties of abstract Schr\"odinger equations with time dependent potentials in vector-valued classes are obtained. The equation involves a possible linear operators…
The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…
In this paper, Hardy's uncertainty principle and unique continuation properties of abstract Schr\"odinger equations in vector-valued classes are obtained
We derive the Mandelstam-Tamm time-energy uncertainty relation for neutrino oscillations in a generic stationary curved spacetime. In particular, by resorting to Stodolsky covariant formula of the quantum mechanical phase, we estimate…
We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on…
A more general measurement disturbance uncertainty principle is presented in a Robertson-Schr\"odinger formulation. It is shown that it is stronger and having nicer properties than Ozawa's uncertainty relations. In particular is invariant…
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric…
In this paper we derive the uncertainty principle for the Loop Quantum Cosmology homogeneous and isotropic FLWR model with the holonomy-flux algebra. The uncertainty principle is between the variables $c$, with the meaning of connection and…
In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for…
The uncertainty principle is a fundamental principle in theoretical physics, such as quantum mechanics and classical mechanics. It plays a prime role in signal processing, including optics, where a signal is to be analyzed simultaneously in…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
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 study the Heisenberg-Pauli-Weyl uncertainty principle and the Caffarelli-Kohn-Nirenberg interpolation inequalities, on metric measure spaces satisfying measure contraction property. Using localization techniques, we show that these…
We present a formulation of the generalised uncertainty principle based on commutator $\left[ {\hat x}^i, {\hat p}_j \right]$ between position and momentum operators defined in a covariant manner using normal coordinates. We show how any…
We investigate properties of the covariance matrix in the framework of non-commutative quantum mechanics for an one-parameter family of transformations between the familiar Heisenberg-Weyl algebra and a particular extension of it. Employing…
It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko-Sereda-Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace-Beltrami operator, which, in…
D.Freed has formulated and proved an index theorem on odd dimensional spin manifolds with boundary. The proof is based on analysis by Calderon and Seeley. In this note we are going to give a proof of this theorem using the heat kernels…
Diverse theories of Quantum Gravity expect modification of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle.It was shown by some authors that the Generalized uncertainty principle…
We provide new uncertainty principles for functions in a general class of Gelfand-Shilov spaces. These results apply, in particular, with the classical Gelfand-Shilov spaces as well as for spaces of functions with weighted Hermite…