Related papers: A statistical theory of structure in many-particle…
In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
Position holds a very special role in understanding the classical behaviour of macroscopic bodies on the basis of quantum principles. This lead us to examine the localised states of a large condensed object in the context of a realistic…
This theoretical paper discusses microscopic models giving rise to special types of order in which conduction electrons are bound together with localized spins to create composite order parameters. It is shown that composite order is…
Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding…
An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Some examples include: sedimenting marine snow particles in lakes and oceans (central to…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
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…
Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…
In the following we undertake to derive quantum theory as a stochastic low-energy and coarse-grained theory from a more primordial discrete and basically geometric theory living on the Planck scale and which (as we argue) possibly underlies…
Small particles transported by a fluid medium do not necessarily have to follow the flow. We show that for a wide class of time-periodic incompressible flows inertial particles have a tendency to spontaneously align in one-dimensional…
The question how complex systems become more organized and efficient with time is open. Examples are, the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, the…
Entropy alone can self-assemble hard particles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Although particle-based molecular simulation…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…