Short periodic orbits theory for partially open quantum maps

We extend the semiclassical theory of short periodic orbits [Phys. Rev. E {\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to classical maps where the trajectories are partially bounced back due to a finite reflectivity $R$. These maps are representative of a class that has many experimental applications. The open scar functions are conveniently redefined, providing a suitable tool for the investigation of these kind of systems. Our theory is applied to the paradigmatic partially open tribaker map. We find that the set of periodic orbits that belong to the classical repeller of the open map ($R=0$) are able to support the set of long-lived resonances of the partially open quantum map in a perturbative regime. By including the most relevant trajectories outside of this set, the validity of the approximation is extended to a broad range of $R$ values. Finally, we identify the details of the transition from qualitatively open to qualitatively closed behaviour, providing an explanation in terms of short periodic orbits.Comment: 6 pages, 4 figure

Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

We study a real, massive Klein-Gordon field in the Poincar\'e fundamental domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincar\'e fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.Comment: 12 pages, 1 figure. In V3: refs. added, introduction and conclusions expande

Reaction rate calculation with time-dependent invariant manifolds

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment

Stellar indices and kinematics in Seyfert 1 nuclei

We present spectra of 6 type 1 Seyfert galaxies, 2 Seyfert 2, a starburst galaxy and a compact narrow line radiogalaxy, taken in two spectral ranges centered around the near--IR CaII triplet (CaT) (at ~8600 Angstroms), and the Mgb stellar feature at 5180 Angstroms. We measured the equivalent width (EWs) of these features and the Fe52 and Fe53 spectral indices. We found that the strength of the CaT in type 1 Seyfert galaxies with prominent central point sources, is larger than what would be expected from the observed strength of the blue indices. This could be explained by the presence of red supergiants in the nuclei of Seyfert 1 galaxies. On the other hand, the blue indices of these galaxies could also be diluted by the strong FeII multiplets that can be seen in their spectra. We have also measured the stellar and gas velocity dispersions of the galaxies in the sample. The stellar velocity dispersions were measured using both, the Mgb and CaT stellar features. The velocity dispersion of the gas in the narrow line region (NLR) was measured using the strong emission lines [OIII] 5007, 4959 and [SIII] 9069. We compare the gas and star velocity dispersions and find that both magnitudes are correlated in Seyfert galaxies. Most of the Seyfert 1 we observe have stellar velocity dispersion somehow greater than that of the gas in the NLR.Comment: To appear in MNRAS, 18 pages, 9 figure

The role of short periodic orbits in quantum maps with continuous openings

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map - a cantor set given by a region of exactly zero reflectivity - prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for step like functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1604.0181