Related papers: Dynamical versions of Hardy's uncertainty principl…
We show the local in time well-posedness of the Prandtl equation for data with Gevrey $2$ regularity in $x$ and $H^1$ regularity in $y$. The main novelty of our result is that we do not make any assumption on the structure of the initial…
We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a…
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…
Recently, Chen et al introduced an alternative form of Hardy's paradox for $2$-settings and high-dimensional systems [Phy. Rev. A 88, 062116 (2013)], in which there is a great progress in improving the maximum probability of the nonlocal…
We prove Hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the Heisenberg group $\mathbb{H}^n$. We prove two versions of such inequalities depending on whether the weights involved are non-homogeneous…
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
The main result of this paper is, that if we suppose that a function is absolutely continuous and uniformly H\"older continuous and that its finite difference function does not oscillate infinitely often on a bounded interval, then the…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
We show how the Schroedinger Uncertainty Relation for a pair of observables can be deduced using the Cauchy-Schwarz inequality plus successive applications of the commutation relation involving the two observables. Our derivation differs…
The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a…
We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability…
An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the…
In this paper we study the uncertainty principle (UP) connecting a function over a finite field and its Mattson-Solomon polynomial, which is a kind of Fourier transform in positive characteristic. Three versions of the UP over finite fields…
By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbf{\Gamma} $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the…
In this note we present a new short and direct proof of L\'{e}vy's continuity theorem in arbitrary dimension $d$, which does not rely on Prohorov's theorem, Helly's selection theorem or the uniqueness theorem for characteristic functions.…
We consider the Cauchy problem for the nonlinear Schr\"odinger equation on $\mathbb{R}^2$, $iu_t + u_{xx} + u_{yy} + \lambda|u|^\sigma u =0$, $\lambda\in \mathbb{R}$, $\sigma>0$. We introduce new functional spaces over which the initial…
In this note we study the Landis conjecture for positive Schr\"odin\-ger operators on graphs. More precisely, we prove a Landis-type result in the form of a decay criterion that ensures when $\mathcal{H}$-harmonic functions for a positive…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
We prove a weak version of Hardy's uncertainty principle using properties of the prolate spheroidal wave functions (PSWFs). We describe the eigenvalues of the sum of a time limiting operator and a band limiting operator acting on L2(R). A…
We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed…