Information-entropic measures for non-zero l states of confined hydrogen-like ions

Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both position ($r$) and momentum ($p$) spaces. In the 1D case, the $n=0$ state is chosen as reference, whereas for a central potential, the respective circular or node-less (corresponding to lowest radial quantum number $n_{r}$) state of a given $l$ quantum number, is selected. Starting from their exact wave functions, expressions of IR in both $r$ and $p$ spaces are obtained in closed analytical forms in all these systems. A careful analysis reveals that, for the 1D QHO, IR in both coordinate spaces increase linearly with quantum number $n$. Likewise, for 3D QHO and PHP, it varies with single power of radial quantum number $n_{r}$ in both spaces. But, in H atom they depend on both principal ($n$) and azimuthal ($l$) quantum numbers. However, at a fixed $l$, IR (in conjugate spaces) initially advance with rise of $n$ and then falls off; also for a given $n$, it always decreases with $l$

Grassmann variables on quantum spaces

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused together.Comment: 42 pages, Latex, crossing symmetries for representations have been simplified, section with general information has been added, typos correcte

Characterizing common cause closedness of quantum probability theories

We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common cause of the correlation. The main result we prove is that a quantum probability space is common cause closed if and only if it has at most one measure theoretic atom. This result improves earlier ones published in Z. GyenisZ and M. Redei Erkenntnis 79 (2014) 435-451. The result is discussed from the perspective of status of the Common Cause Principle. Open problems on common cause closedness of general probability spaces $(\mathcal{L},\phi)$ are formulated, where $\mathcal{L}$ is an orthomodular bounded lattice and $\phi$ is a probability measure on $\mathcal{L}$.Comment: Submitted for publicatio