Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincare surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy εc, for ε 〈 εc, the system is near-integrable, and as the decrease of ε the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if ε 〉 εc, with the increase of ε, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.

The dynamical properties of a Rydberg hydrogen atom between two parallel metal surfaces

This paper presents the dynamical properties of a Rydberg hydrogen atom between two metal surfaces using phase space analysis methods. The dynamical behaviour of the excited hydrogen atom depends sensitively on the atom-surface distance d. There exists a critical atom-surface distance dc = 1586 a.u. When the atom-surface distance d is larger than the critical distance de, the image charge potential is less important than the Coulomb potential, the system is near-integrable and the electron motion is regular. As the distance d decreases, the system will tend to be non-integrable and unstable, and the electron might be captured by the metal surfaces.

Evolution of Periodic Orbits in the Sun-Saturn System

We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.

Analysis of Effect of Oblateness of Smaller Primary on the Evolution of Periodic Orbits

Evolution of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of oblateness of smaller primary on these orbits are considered. It is observed that oblateness of smaller primary has substantial effect on period, orbit’s shape, size and their position in the phase space. Since these orbits can be used for the design of low energy transfer trajectories, so perturbations due to planetary oblateness has to be understood and should be taken care of during trajectory design. In this paper, detailed stability analysis of periodic orbit having three loops is given for A2 = 0.0001.

Evolution of the “f” Family Orbits in the Photo Gravitational Sun-Saturn System with Oblateness

We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.

Analysis of Effect of Solar Radiation Pressure of Bigger Primary on the Evolution of Periodic Orbits

Evolution of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of solar radiation pressure of bigger primary and actual oblateness of smaller primary on these orbits areconsidered. It is observed that solar radiation pressure of bigger primary has substantial effect on period, orbit’s shape, size and their position in the phase space. Since these orbits can be used for the design of low energy transfer trajectories, so perturbations due to solar radiation pressure has to be understood and should be taken care of during trajectory design. It is also verified that stability of such orbits are negligible so they can be used as transfer orbit. For each pair of solar radiation pressure q and Jacobi constant C we get two separatrices where stability of island becomes zero. In this paper, detailed stability analysis of periodic orbit having two loops is given when q = 0.9845.

Effect of intramolecular energy transfer on the rate of unimolecular isomerization: HCN --HNC

This paper reports calculations of the rate of isomerization of HCN - HCN based on the theory of Gary and Rice as extended by Zhao and Rice. The major task is to determine the effect of intramolecular energy transfer on the prediction of the rate of isomerization. Both the full three-dimensional (3D) system and the reduced two-dimensional (2D) system obtained from freezing CN bond at 1.159 A are analyzed to check the validity of the freezing bond approximation. Meanwhile, RRKM rates are calculated to test RRKM choice of the transition state by comparing to Gary-Rice three-state model. The comparison shows that the rates from 2D model and 3D model are differing up to 20% with 2D rates consistently larger. The intramolecular energy transfer modifies the isomerization rate for HCN system up to 30% that is modestly small by the expectation. The isomerization rate predicted from RRKM theory is greater than those of Gary-Rice three-state model theory up to 65%, and it overstimates the rates under all considerations, including the contribution from intramolecular energy transfer, for the studied system by about a factor of 2.