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Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable…

A model Hamiltonian for the reaction CH$_4^+ \rightarrow$ CH$_3^+$ + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose…

We consider the roaming mechanism for chemical reactions under the nonholonomic constraint of constant kinetic energy. Our study is carried out in the context of the Hamiltonian isokinetic thermostat applied to Chesnavich's model for an…

We provide a dynamical interpretation of the recently identified `roaming' mechanism for molecular dissociation reactions in terms of geometrical structures in phase space. These are NHIMs (Normally Hyperbolic Invariant Manifolds) and their…

We consider the existence of invariant manifolds in phase space governing reaction dynamics in situations where there are no saddle points on the potential energy surface in the relevant regions of configuration space. We point out that…

Roaming has been proposed as a possible mechanism contributing to molecular dissociation in which the fragments can move around one another at relatively large intermolecular distances before separating entirely. While roaming, there is…

Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invariant structures have already been identified. In this case we…

In this paper we analyze a two degree of freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical…

Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from…

This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial…

The ring-polymer molecular dynamics (RPMD) was used to calculate the thermal rate coefficients of the two-channel roaming reaction H + MgH. Both reaction channels, tight and roaming, are explicitly considered. This is a pioneering attempt…

We study the phase space geometry associated with index 2 saddles of a potential energy surface and its influence on reaction dynamics for $n$ degree-of-freedom (DoF) Hamiltonian systems. For index 1 saddles of potential energy surfaces…

A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…

We introduce a model of Poincar\'e mappings which represents hierarchical structure of phase spaces for systems with many degrees of freedom. The model yields residence time distribution of power type, hence temporal correlation remains…

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori it is possible to define phase space dividing…

We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the hydrogen chromophore's vibrational motion in the molecule $CF_3CHFI$. The original model has 4 degrees of freedom, three positions and one representing…

We consider a simple model of lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. Internal dynamics of the atom is governed by the laser field…

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and…

Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…

A reduced two dimensional model is used to study Ketene isomerization reaction. In light of recent results by Ulusoy \textit{et al.} [J.\ Phys.\ Chem.\ A {\bf 117}, 7553 (2013)], the present work focuses on the generalization of the roaming…