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

The scar mechanism revisited

Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to accumulate quantum density along the orbit by a constructive interference mechanism when the appropriate quantization (on the action of the scarring orbit) is fulfilled. Other quantized phase space circuits, such as those defined by homoclinic tori, are also important in the coherent transport of quantum density in chaotic systems. The relationship of this secondary quantum transport mechanism with the standard mechanism for scarring is here discussed and analyzed.Comment: 6 pages, 6 figure

Compact UWB Monopole for Multilayer Applications

A novel compact, dual layer UWB monopole antenna is presented. This low profile ultra-wideband antenna is fed by a 50 ? shielded strip-line with an array of metal vias making the conducting walls. A printed disc monopole with a circular cut is the radiating element. The dual layer, shielded strip line feed allows for integration in multilayer technologies. The ultra-wideband, monopole characteristics of the antenna are confirmed experimentally