Related papers: Some Comments on Categories, Particles and Interac…
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.
A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…
I review various theory issues in diffraction that have been presented and discussed in the working group on diffractive interactions, and a few points concerning the comparison of theory with data.
Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
An approach for understanding the behavior of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are…
Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…