A compact review is given, and a few new numerical results are added to the recent studies of the q-pointed one-dimensional star-shaped quantum graphs. These graphs are assumed endowedwith certain specific, manifestly ...

We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0) is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and ...

We show that isomorphism of effect algebras preserves properties of effect algebras derived from effect algebraic sum ? of elements. These are partial order, order convergence, order topology, existence of states and other ...

We show that, contrary to a claim made in arXiv:1011.0645, the von Neumann-Winger bound states that lie in the continuum of the scattering states are fundamentally different from Naimark’s spectral singularities.

Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have ...

We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional ...

In this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when ...

The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space ...

The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms ...

According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees ...