We present ultimate version of no-hidden-variables theorem. We shall derive a proposition under the existence of the Bloch sphere in a single spin-1/2 system. The existence of a single classical probability space for measurement outcome within the formalism of von Neumann’s projective measurement cannot coexist with the proposition. Namely, we have to give up the existence of such a classical p...

This paper reviews recent attempts to describe the twoand threequbit Hilbert space geometries with the help of Hopf fibrations. In both cases, it is shown that the associated Hopf map is strongly sensitive to states entanglement content. In the two-qubit case, a generalization of the one-qubit celebrated Bloch sphere representation is described.

Fractional-order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As magnetic resonance imaging is applied with increasing temporal and spatial resolution, the spin dynamics is being examined more closely; such examinations exte...

wannier90 is a program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWFs in real space. This done in the space of unitary matrices that describe rotations of the Bloch bands at each kpoint. As a result, wannier90 is independen...