相关论文: Towards "dynamic domains": totally continuous coco…

Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…

This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary…

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…

Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…

In this work we build a quantum logic that allows us to refer to physical magnitudes pertaining to different contexts from a fixed one without the contradictions with quantum mechanics expressed in no-go theorems. This logic arises from…

The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…

It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and…

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…

A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…

Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…

Our subject is that of categories, functors and distributors enriched in a base quantaloid Q. We show how cocomplete Q-categories are precisely those which are tensored and conically cocomplete, or alternatively, those which are tensored,…

It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…

Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…

Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…

The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…