Formalization of Bohr’s Contextuality Within the Theory of Open Quantum Systems

Journal of Russian Laser Research - In quantum physics, the notion of contextuality has a variety of interpretations, which are typically associated with the names of their inventors, say, Bohr,...     

Recursion over partitions

The paper demonstrates how to apply a recursion on the fundamental concept of number. We propose a generalization of the partitions of a positive integer n, by defining new combinatorial objects, namely sub-partitions. A recursive formula is suggested, designated to solve the associated enumeration problem. It is highlighted that sub-partitions provide a good language to study rooted phylogenetic trees.     

T-functions revisited: new criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and a fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.     

Vladimir Sergeevich Anashin

On the occasion of the 60th birthday of Professor Vladimir Sergeevich Anashin, we present a review of his significant scientific research and related activities.     

<Emphasis Type="Italic">p</Emphasis>-Adic mathematical physics and B. Dragovich research

We present a brief review of some parts of p-adic mathematical physics related to the scientific work of Branko Dragovich on the occasion of his 70th birthday.     

Two-particle wave function as an integral operator and the random field approach to quantum correlations

We propose a new interpretation of the wave function Ψ (x, y) of a two-particle quantum system, interpreting it not as an element of the functional space L ₂ of square-integrable functions, i.e., as a vector, but as the kernel of an integral (Hilbert-Schmidt) operator. The first part of the paper is devoted to expressing quantum averages including the correlations in two-particle systems using the wave-function operator. This is a new mathematical representation in the framework of conventional quantum mechanics. But the new interpretation of the wave function not only generates a new mathematical formalism for quantum mechanics but also allows going beyond quantum mechanics, i.e., representing quantum correlations (including those in entangled systems) as correlations of (Gaussian) random fields.