Related papers: On Many Body System Interactions
This is a light survey article about the origins of contact and symplectic topology in dynamics and the more recent developments in the field. In lieu of formulas, numerous anecdotes are given.
Few physical systems with topologies more complicated than simple gaussian linking have been explored in detail. Here we focus on examples with higher topologies in non-relativistic quantum mechanics and in QCD.
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
We explore the possibility that physical phenomena arising from interacting multi-particle systems, can be usefully interpreted in terms of multi-player games. We show how non-cooperative phenomena can emerge from Ising Hamiltonians, even…
We will study a class of system composed of interacting unicyclic machines placed in contact with a hot and cold thermal baths subjected to a non-conservative driving worksource. Despite their simplicity, these models showcase an intricate…
Several interdisciplinary areas have appeared at the interface between biological and physical sciences. In this work, we suggest a complex network-based methodology for analyzing the interrelationships between some of these…
Recent developments in the area of soft interactions and multiparticle correlations are reviewed, including higher harmonic flows conjectured to result from the initial-state geometry which might coincide with some jet-like correlation…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
We survey some results on toric topology.
The formal structure of geometrical thermodynamics is reviewed with particular emphasis on the geometry of equilibria submanifolds. On these submanifolds thermodynamic metrics are defined as the Hessian of thermodynamic potentials. Links…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
In a many body system, constituents interact with each other, forming a recursive pattern of interaction and giving rise to many interesting phenomena. Based upon concepts of the modern many body theory, a model for a generic many body…
We study some topological properties of attractors.
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number of additional topological invariants for cholesteric…
This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…