Hidden symmetries, instabilities, and current suppression in Brownian ratchets

The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of {\it hidden} symmetries, which escape the identification by the standard symmetry analysis, and require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.Comment: To appear in Phys. Rev. Let

Asymptotic theory of quasiperiodically driven quantum systems

The theoretical treatment of quasi-periodically driven quantum systems is complicated by the inapplicability of the Floquet theorem, which requires strict periodicity. In this work we consider a quantum system driven by a bi-harmonic driving and examine its asymptotic long-time limit, the limit in which features distinguishing systems with periodic and quasi-periodic driving occur. Also, in the classical case this limit is known to exhibit universal scaling, independent of the system details, with the system's reponse under quasi-periodic driving being described in terms of nearby periodically driven system results. We introduce a theoretical framework appropriate for the treatment of the quasi-periodically driven quantum system in the long-time limit, and derive an expression, based on Floquet states for a periodically driven system approximating the different steps of the time evolution, for the asymptotic scaling of relevant quantities for the system at hand. These expressions are tested numerically, finding excellent agreement for the finite-time average velocity in a prototypical quantum ratchet consisting of a space-symmetric potential and a time-asymmetric oscillating force

An excess electron at polyethylene/vacuum interfaces using a reaction-field technique

We study the surface states of an excess electron at polyethylene/vacuum interfaces using an accurate reaction-field method, specifically designed to take into account the long range interaction of the excess electron and the dielectric surface. The method is shown to validate the energy levels recently reported with a simple perturbation theory scheme, while providing a better description of the wave function at the vacuum. The use of a single particle pseudopotential allows the simulation of large interface samples, showing distinct differences between the electron surface states at amorphous and crystalline interfaces due to their different atomic density.Ministerio de Economía y Competitividad of Spain, Grant No. FIS2016-80244

Irrationality and quasiperiodicity in driven nonlinear systems

We analyse the relationship between irrationality and quasiperiodicity in nonlinear driven systems. To that purpose we consider a nonlinear system whose steady-state response is very sensitive to the periodic or quasiperiodic character of the input signal. In the infinite time limit, an input signal consisting of two incommensurate frequencies will be recognised by the system as quasiperiodic. We show that this is in general not true in the case of finite interaction times. An irrational ratio of the driving frequencies of the input signal is not sufficient for it to be recognised by the nonlinear system as quasiperiodic, resulting in observations which may differ by several orders of magnitude from the expected quasiperiodic behavior. Thus, the system response depends on the nature of the irrational ratio, as well as the observation time. We derive a condition for the input signal to be identified by the system as quasiperiodic. Such a condition also takes into account the sub-Fourier response of the nonlinear system.Comment: accepted in Phys. Rev. Let

Brillouin propagation modes of cold atoms in dissipative optical lattices

An exact series expansion of the average velocity of cold atoms in dissipative optical lattices under probe driving, based on the amplitudes of the excited atomic density waves, is derived from the semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. This expansion permits the identification of the precise contribution to the current of a propagating atomic wave for the specific driving, as well as providing the general threshold for the transition into the regime of infinite density

Comment on “Markovian approximation in a coarse-grained description of atomic systems” [J. Chem. Phys.125, 204101 (2006)]

The authors concluded that the coarse-graining dynamics of a one-dimensional chain of oscillators interacting through Lennard–Jones potentials is Markovian, in contrast with the situation observed for harmonic lattices. However, with the help of a novel equation that relates the correlation of forces and momenta, I show that this conclusion is drawn from an incorrect analysis of the simulation data.Dirección General de Enseñanza Superior of Spain Grant No. FIS2005-0288

Aprenentatge automàtic per anàlisis de imatges hiperespectrals

With the advent of less expensive hyperspectral cameras, now hyperspectral images are increasingly used in many fields and thus, first, traditional machine learning tools should be exploited for its analysis. The project is focused on target detection to find similarities within a hyperspectral image, where we first implement the AMF, SAM and OSP detectors, where the OSP is shown to be superior. With this results, there are some distractors and noise items that the detectors are not capable of disregard. This is why we use machine learning, specifically K-Means as clustering technique, in order to remove useless information and possible noise, and then to apply the detectors only on the target cluster. Using K-Means + AMF/SAM Detector improves the results. On the contrary, with K-Means + OSP Detector the results get worse since K-Means provides a good clustering and thus, the target pixels are considered as background subspace instead of anomalies. Using new data, where K-Means does not provide good clustering, K-Means + OSP Detector provides better results than before although K-Means + AMF/SAM Detector stills being a bit better.Con la llegada de cámaras hiperespectrales menos caras, ahora las imágenes hiperespectrales se utilizan cada vez más en muchos campos y, por lo tanto, en primer lugar, herramientas tradicionales del aprendizaje automático deberían ser explotadas para su análisis. El proyecto está enfocado en la detección de objetivos para encontrar similitudes en una imagen hiperespectral, donde primero implementamos los detectores AMF, SAM y OSP siendo el OSP el que mejor funciona. Con estos resultados, hay algunos distractores y elementos de ruido que los detectores no son capaces de ignorar. Es por eso que usamos el aprendizaje automático, especialmente K-Means como técnica de agrupación, para eliminar información inútil y posible ruido, y entonces aplicar los detectores solo en el grupo donde esta el objetivo. Utilizando K-Means + Detector AMF/SAM los resultados mejoran. En cambio, con K-Means + Detector OSP los resultados empeoran ya que K-Means hace un buena agrupación, y por lo tanto, los píxeles objetivo son considerados como subespacio de fondo en vez de anomalías. Usando nuevos datos donde K-Means no proporciona buena detección, K-Means + Detector OSP proporciona mejores resultados aunque K-Means + Detector AMF/SAM sigue siendo un poco mejor.Amb l’arribada de càmeres hiperespectrals menys cares, ara les imatges hiperespectrals s’utilitzen cada cop més en moltes àrees i, per tant, en primer lloc, eines tradicionals de l’aprenentatge automàtic haurien de ser explotades per al seu anàlisis. El projecte es centra en la detecció d’objectius per trobar similituds en una imatge hiperespectral, on primer implementem els detectors AMF, SAM i OSP, sent l’OSP el que funciona millor. Amb aquests resultats, hi ha alguns distractors i elements de soroll que els detectors no són capaços d’ignorar. Es per això que utilitzem l’aprenentatge automàtic, especialment ´ K-Means com a tècnica d’agrupació, per tal d’eliminar informació inútil i possible soroll, i llavors aplicar els detectors només al grup on està l’objectiu. Utilitzant K-Means + Detector AMF/SAM els resultats milloren. En canvi, amb K-Means + Detector OSP els resultats empitjoren ja que K-Means fa un agrupament bo i, per tant, els pixels objectius són considerats com a subespai de fons en comptes d’anomalies. Utilitzant dades noves on K-Means no proporciona bons resultats, K-Means + Detector OSP ofereix millors resultats encara que K-Means + Detector AMF/SAM segueix sent una mica millor

Thermal equilibrium in Einstein's elevator

We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the J\"uttner function -- originally derived for a flat spacetime -- via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified J\"uttner function, which was initially proposed as an alternative to the J\"uttner function