Related papers: A Lax Functorial Definition of Open Dynamics
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…
This paper discusses some links properties of operators with the well- known physical concepts of hyperstability, passivity, energy dissipativeness and conservativeness with positive realness properties of the transfer functions in linear…
We use the Kossakowski-Lindblad-Davies formalism to consider an open system defined as the Markovian extension of one-mode quantum oscillator S, perturbed by a piecewise stationary harmonic interaction with a chain of oscillators C. The…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
A introduction into density-functional theory and electronic structure methods is given, that aims at providing an intuitive understanding of the underlying concepts for the novice as well as an entry point towards the more advanced…
We analyse the flow of information in multiplex networks by means of the communicability function. First, we generalize this measure from its definition from simple graphs to multiplex networks. Then, we study its relevance for the analysis…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…
Dynamical maps are the principal subject of the open system theory. Formally, the dynamical map of a given open quantum system is a density matrix transformation that takes any initial state and sends it to the state at a later time.…
An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…
The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics,…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
Lax extensions of set functors play a key role in various areas including topology, concurrent systems, and modal logic, while predicate liftings provide a generic semantics of modal operators. We take a fresh look at the connection between…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
A description of many constituent (particle) systems with fuzzy initial conditions is proposed with the help of the field language. In this language correlation functions are defined and equations for them are derived in the free Fock…
We explain why the macroscopic fluctuations of deterministic local collision dynamics should be characterized by a non strictly convex functional.
The possibility for humans to interact with physical or virtual systems using gestures has been vastly explored by researchers and designers in the last twenty years to provide new and intuitive interaction modalities. Unfortunately, the…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…