Related papers: On the relation between action and linking

In this paper, we revisit the concepts of the reactivity map and the reactivity bands as an alternative to the use of perturbation theory for the determination of the phase space geometry of chemical reactions. We introduce a reformulated…

A hyperbolic set on a compact manifold M, satisfies the property: given two of your any points p and q, such that for all positive \epsilon>0, there is a trajectory in the hyperbolic set from a point \epsilon-close to p to a point…

In the following article, we construct an interaction model (a variant of the SIR-model) of general language change. In the context of language change it is desirable to deduce the long-term behaviour of the corresponding dynamical system…

This note was written for the proceedings of the conference "Symplectic Geometry and Anosov Flows" held in Heideleberg in July 2024. It is meant as an invitation to the study of certain families of contact structures, centering around the…

Standard statistical mechanics of conservative systems relies on the symplectic geometry of the phase space. This is exploited to derive Hamilton's equations, Liouville's theorem and to find the canonical invariant measure. In this work we…

The scale dependence of an effective average action for mesons and quarks is described by a nonperturbative flow equation. The running couplings lead to spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling between…

We consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a…

We derive an action-flux formula to compute the volumes of lobes quantifying transport between past- and future-invariant Lagrangian coherent structures of n-dimensional, transitory, globally Liouville flows. A transitory system is one that…

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…

We propose an equation that describes the shape of the driven contact line in dynamics in the presence of an arbitrary (possibly random) distribution of the surface defects. It is shown that the triple contact line depinning differs from…

After a brief review of the field formulations and the relativistic non-instantaneous action-at-a-distance formulations of some well known classical theories, we study Rivacoba's generalization of a theory with a linearly rising potential…

Cylindrical contact homology is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings and Nelson. We study this invariant for a general…

We consider homotopy actions of a Lie algebroid on a graded manifold, defined as suitable $L_{\infty}$-algebra morphisms. On the "semi-direct product" we construct a homological vector field that projects to the Lie algebroid. Our main…

Using the world-line method we resum the scalar one-loop effective action. This is based on an exact expression for the one-loop action obtained for a background potential and a Taylor expansion of the potential up to quadratic order in…

We suggest a new random model for links based on meander diagrams and graphs. We then prove that trivial links appear with vanishing probability in this model, no link $L$ is obtained with probability 1, and there is a lower bound for the…

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $\mu$, random walks with…

In the paper we consider non-relativistic analog of the Nambu-Jona-Lasinio model and demonstrate, by this most simplified example, the method of dynamical mappings of Heisenberg fields on "physical" fields. We obtain the expressions for one…

We present and demonstrate a version of Levinson's theorem especially dedicated to the asymptotic behavior of form factor phases. Indeed, as required by analyticity, form factors are multi-valued complex functions of a square four-momentum…

In 1987, Liechtenstein et al. came up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of the magnetic…

An overview of a microscopic framework based on the Hartree-Fock description of the mean field is presented which, starting from an effective interaction allows a description of collective motions. A study of the isotope shifts in the Pb…