Related papers: Jointly Equivariant Dynamics for Interacting Parti…
Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $\chi(M)\ne 0$. We show that if $G$ is a finite group of 2-rank $\le 1$ which admits a homologically…
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…
It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
Normal mode dynamics are ubiquitous underlying the motions of diverse systems from rotating stars to crystal structures. These behaviors are composed of simple collective motions of particles which move with the same frequency and phase,…
We investigate the static and the dynamic properties of an binary, equimolar, size-symmetric mixture of ultrasoft particles in the vicinity of the critical point of the system. Based on the generalized exponential potential (GEM) of order…
Let $G$ be a noncompact semisimple Lie group, $\Gamma$ be an irreducible cocompact lattice in $G$, and $P<G$ be a minimal parabolic subgroup. We consider the dynamics of $P$ acting on $G/\Gamma$ by left translation. For any infinite subset…
We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…
In this article, we study the dynamics of translations of an element of a semisimple Lie group $G$ acting on its maximal compact subgroup $K$. First, we extend to our context some classical results in the context of general flag manifolds,…
In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence…
We investigate dynamics and interactions of particles levitated and trapped by the thermophoretic force in a vacuum cell. Our analysis is based on footage taken by orthogonal cameras that are able to capture the three dimensional…
For noncompact semisimple Lie groups $G$ we study the dynamics of the actions of their discrete subgroups $\Gamma<G$ on the associated partial flag manifolds $G/P$. Our study is based on the observation that they exhibit also in higher rank…
The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
A surface in a three-dimensional metric Lie group $G$ is said invariant if it is invariant with respect to a one-dimensional subgroup $\Gamma$ of the isometry group of $G$. Is this work we focus on unimodular metric Lie groups $G$ that can…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated…
The effects of purely elastic collisions on the dynamics of heavy inertial particles is investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of inter-particle separations and relative…
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…