The well-known second moment Heisenberg-Weyl inequality (or uncertainty relation) states: Assume that f : R → C is a complex valued function of a random real variable x such that f ∈ L(R), where R = (−∞,∞). Then the product of the second moment of the random real x for |f | and the second moment of the random real ξ for ∣∣∣f̂ ∣∣∣2 is at least ER,|f |2 / 4π, where f̂ is the Fourier transform of f ...

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis        

A quantitative estimation of quantum discord is performed for a Heisenberg spin 1/2 dimer compound (NH4CuPO4, H2O) by means of experimental magnetic and thermal measurements. Magnetic susceptibility and specific heat data were collected for NH4CuPO4, H2O and analyzed within the framework of the Heisenberg isolated dimer model. Internal energy as a function of temperature is obtained by integrat...

We prove a quantitative stability result for the Heisenberg–Pauli–Weyl inequality. This leads to next, and next-to-next order correction terms in

We show a sharp relationship between the existence of space filling mappings with an upper gradient in a Lorentz space and the Poincaré inequality in a general metric setting. As key examples, we consider these phenomena in Cantor diamond spaces and the Heisenberg groups.

We formulate the isoperimetric problem for the class of C2 smooth cylindrically symmetric surfaces in the Heisenberg group in terms of Legendrian foliations. The known results for the sub-Riemannian isoperimetric problem yield a new isoperimetric inequality in the plane: For any strictly convex, C2 loop γ ∈ R2, bounding a planar region ω, we have

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its applications to time operators and abstract Dirac operators are also investigated.

The uncertainty principle is a cornerstone in quantum phsysics. However, its principles play an equally monumental role in harmonic analysis. To put it in one sentence: A nonzero function and its Fourier transform cannot both be sharply localized. While Heisenberg gave a clear physical interpretation of the uncertainty principal in 1927 in [7], it contains little mathematical precision. This wa...