Related papers: Restricted three body problems at the nanoscale
The existence of a system of short-live discrete volume-localized electron quantum levels in positively charged fullerenes is theoretically and numerically demonstrated using the example of fullerenes C60 and C20. Unlike well-studied…
Using a unified macroscopic QED formalism, we derive an integral equation for the van der Waals energy of a two-level atomic system near a carbon nanotube. The equation is valid for both strong and weak atom-vacuum-field coupling. By…
A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the…
Considering C$_{60}$ as a model system for describing field emission from the extremity of a carbon nanotip, we explore electron emission from this fullerene excited by an intense, near-infrared, few-cycle laser pulse…
The restricted circular three-body problem is considered for the following parameter values $C=3.03$, $\mu=0.0009537$ - the values for {\em Oterma} comet in the Sun-Jupiter system. We present a computer assisted proof of an existence of…
We treat three-dimensional bosonic clusters wih up to N=40 atoms, interacting additively through two-body Van der Waals potentials, in the near-threshold regime. Our study inludes super-borromean systems with N atoms for which all…
We study equations for the mechanical movement of chains of identical particles in the plane interacting with their nearest-neighbors by bond stretching and by van der Waals and Coulomb forces. We find collinear and circular equilibria as…
Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate…
Endohedral fullerenes, or endofullerenes, are chemical systems of fullerene cages encapsulating single atoms or small molecules. These species provide an interesting challenge of Potential Energy Surface (PES) determination as examples of…
This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system…
The large distance behavior of weakly bound three-body systems is investigated. The Schr\"{o}dinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The…
I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
We investigate three-boson recombination of equal mass systems as function of (negative) scattering length, mass, finite energy, and finite temperature. An optical model with an imaginary potential at short distance reproduces experimental…
We investigate the prospects of combining a standard momentum space approach for ultracold three-body scattering with efficient coordinate space schemes to solve the underlying two-body problem. In many of those schemes the two-body problem…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
The three body problem is a special case of the n body problem where one takes the initial positions and velocities of three point masses and attempts to predict their motion over time according to Newtonian laws of motion and universal…
Phase transition in fullerenes C60 and C240 are investigated by means of constant-temperature molecular dynamics simulations. In the phase transition region, the assembly (and fragmentation) of the C60 cage from (and to) the gaseous state…
We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…