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

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

Phosphonium dicyanamide ionogel incorporating bromophenol blue dye as a versatile platform for monitoring pH in solution

Online monitoring of pH levels in different environments such as bio-engineering and chemistry is vital for effective control of many critical industrial processes. The most common chemical parameter monitored is pH, and there is an increasing interest in the fabrication of robust, cheap and versatile pH sensing materials that can be easily integrated within existing industrial technologies. Ideally these materials present low fouling and do not require calibration, thus minimising manual attention over long operational intervals. In this work we present an innovative material (ionogel) that integrates pH-sensing capabilities for continuously measuring pH during chemical or biological processes. The ionogel is a solid, flexible and easily to pattern material generated using tetrabutylphosponium dicyanamide ionic liquid, hydrogel polymer (N-isopropylacrylamide and N,N-methylene-bis(acrylamide)) and a pH sensitive dye (Bromophenol Blue). Figure 1 shows the UV spectra of the ionogel-dye in an acidic and a basic pH environment as well as the pictures of the ionogels. A substantial colour variation is observed as the pH changes that can be monitored visually or optically. We incorporated the photoresponsive dye during photo-polymerisation of the monomer to improve stability, for example, by preventing leaching of the dye from the ionogel into the sample phase. This strategy was not found to inhibit the sensitivity of the optical response

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

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

Real-space study of the growth of magnesium on ruthenium

The growth of magnesium on ruthenium has been studied by low-energy electron microscopy (LEEM) and scanning tunneling microscopy (STM). In LEEM, a layer-by-layer growth is observed except in the first monolayer, where the completion of the first layer in inferred by a clear peak in electron reflectivity. Desorption from the films is readily observable at 400 K. Real-space STM and low-energy electron diffraction confirm that sub-monolayer coverage presents a moir\'e pattern with a 1.2 nm periodicity, which evolves with further Mg deposition by compressing the Mg layer to a 2.2 nm periodicity. Layer-by-layer growth is followed in LEEM up to 10 ML. On films several ML thick a substantial density of stacking faults are observed by dark-field imaging on large terraces of the substrate, while screw dislocations appear in the stepped areas. The latter are suggested to result from the mismatch in heights of the Mg and Ru steps. Quantum size effect oscillations in the reflected LEEM intensity are observed as a function of thickness, indicating an abrupt Mg/Ru interface.Comment: 21 pages, 10 figure

Maximum population transfer in a periodically driven two-level system

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular modelComment: 7 pages, 6 figure

- A COMPUTATIONAL APPROACH TO THE FUNDAMENTAL THEOREM OF ASSET PRICING IN A SINGLE-PERIOD MARKET.

In this paper we provide a new approach to the Fundamental Theorem of As-set Pricing. The proofof this result is usually based on Projection (Separation) Theorems and is far more intuitive. Ourapproach follow the relation between the projection problem an equivalent least squares problem.More precisely, we will use and iterative procedure in order to obtain solutions of a bounded leastsquare problem. This solutions will give, under some conditions, either the state price vector orthe arbitrage opportunity of the problem under consideration.Asset Pricing; Arbitrage; Mathematical Finance

Concept and development of an autonomous wearable micro-fluidic platform for real time pH sweat analysis

In this work the development of an autonomous, robust and wearable micro-fluidic platform capable of performing on-line analysis of pH in sweat is discussed. Through the means of an optical detection system based on a surface mount light emitting diode (SMD LED) and a light photo sensor as a detector, a wearable system was achieved in which real-time monitoring of sweat pH was performed during 55 minutes of cycling activity. We have shown how through systems engineering, integrating miniaturised electrical components, and by improving the micro-fluidic chip characteristics, the wearability, reliability and performance of the micro-fluidic platform was significantly improved

Early forest fire detection by vision-enabled wireless sensor networks

Wireless sensor networks constitute a powerful technology particularly suitable for environmental monitoring. With regard to wildfires, they enable low-cost fine-grained surveillance of hazardous locations like wildland-urban interfaces. This paper presents work developed during the last 4 years targeting a vision-enabled wireless sensor network node for the reliable, early on-site detection of forest fires. The tasks carried out ranged from devising a robust vision algorithm for smoke detection to the design and physical implementation of a power-efficient smart imager tailored to the characteristics of such an algorithm. By integrating this smart imager with a commercial wireless platform, we endowed the resulting system with vision capabilities and radio communication. Numerous tests were arranged in different natural scenarios in order to progressively tune all the parameters involved in the autonomous operation of this prototype node. The last test carried out, involving the prescribed burning of a 95 x 20-m shrub plot, confirmed the high degree of reliability of our approach in terms of both successful early detection and a very low false-alarm rate. Journal compilationMinisterio de Ciencia e Innovación TEC2009-11812, IPT-2011-1625-430000Office of Naval Research (USA) N000141110312Centro para el Desarrollo Tecnológico e Industrial IPC-2011100