Quantum manifestations of chaos in elastic atom-surface scattering

Quantum manifestations of chaos in the diffraction of atoms from corrugated surfaces, for a range of initial conditions easily attainable in scattering experiments, are presented and discussed. The appearance of strong oscillations in diffraction patterns is shown to be directly related to the presence of classical chaos and threshold effects. We also show that the autocorrelation function for some of the collision S-matrix elements over incident angles is sensitive to the character, hyperbolic or nonhyperbolic, of the underlying chaotic dynamics, in agreement with general semiclassical arguments for unbound chaotic systems. © 2001 The American Physical SocietyThis work was supported by DGES (Spain) under Contract Nos. PB95-71 and PB98-115 and the European Contract No. HPRN-CT-1999-00005. R.G. acknowledges financial support from CAM (Spain).Peer Reviewe

Hamiltonian theory for vibrational line shapes of atoms adsorbed on surfaces

An analytical theory which was based on a Hamiltonian equivalent of the generalized Langevin equation, for the line shape, temperature-dependent shift and broadening of the translational or T-mode peak is presented. The theory can be used to infer physical parameters of the adatom-surface interaction. For the line shape a first-order perturbative solution of the normal-mode coordinates was used. For the shift and broadening, a perturbative expansion in the instantaneous system frequency was employed.This work has been supported in part by DGICYT (Spain) under Contract No. BFM2001-2179. R.G. and J.L.V. thank the Ministry of Science and Technology (Spain) for a Ramón y Cajal Contract and a predoctoral F.P.I. grant, respectively. This work has also been supported by grants from the Israel Science Foundation, the Minerva Foundation (Munich) and the Volkswagen Foundation.Peer Reviewe

Kramers' turnover theory for diffusion of Na atoms on a Cu(001) surface measured by He scattering

12 pages, 7 figures.The diffusion of adatoms and molecules on a surface at low coverage can be measured by helium scattering. The experimental observable is the dynamic structure factor. In this article, we show how Kramers' turnover theory can be used to infer physical properties of the diffusing particle from the experiment. Previously, Chudley and Elliot showed, under reasonable assumptions, that the dynamic structure factor is determined by the hopping distribution of the adsorbed particle. Kramers' theory determines the hopping distribution in terms of two parameters only. These are an effective frequency and the energy loss of the particle to the bath as it traverses from one barrier to the next. Kramers' theory, including finite barrier corrections, is tested successfully against numerical Langevin equation simulations, using both separable and nonseparable interaction potentials. Kramers' approach, which really is a steepest descent estimate for the rate, based on the Langevin equation, involves closed analytical expressions and so is relatively easy to implement. Diffusion of Na atoms on a Cu(001) surface has been chosen as an example to illustrate the application of Kramers' theory.This work has been supported in part by DGICYT (Spain) under Contract No. BFM2001-2179. R.G. and J.L.V. thank the Minister of Science and Technology (Spain) for a Ramón y Cajal Contract and a predoctoral F.P.I. grant. This work has also been supported by grants from the Israel Science Foundation, the Minerva Foundation (Munich), and the Volkswagen Foundation.Peer reviewe

Global variability in gene expression and alternative splicing is modulated by mitochondrial content

Noise in gene expression is a main determinant of phenotypic variability. Increasing experimental evidence suggests that genome-wide cellular constraints largely contribute to the heterogeneity observed in gene products. It is still unclear, however, which global factors affect gene expression noise and to what extent. Since eukaryotic gene expression is an energy demanding process, differences in the energy budget of each cell could determine gene expression differences. Here, we quantify the contribution of mitochondrial variability (a natural source of ATP variation) to global variability in gene expression. We find that changes in mitochondrial content can account for ∼50% of the variability observed in protein levels. This is the combined result of the effect of mitochondria dosage on transcription and translation apparatus content and activities. Moreover, we find that mitochondrial levels have a large impact on alternative splicing, thus modulating both the abundance and type of mRNAs. A simple mathematical model in which mitochondrial content simultaneously affects transcription rate and splicing site choice can explain the alternative splicing data. The results of this study show that mitochondrial content (and/or probably function) influences mRNA abundance, translation, and alternative splicing, which ultimately affects cellular phenotypeThe authors would like to thank the Ministerio de Economia y Competitividad (Spain) (Grant numbers BFU2009-10792 and BFU2013-45918-R) and The Medical Research Council (U.K.) for supporting this work. We thank the Fundação Ciência e Tecnologia (Portugal) for funding R.P.N. A.R. held a postgraduate fellowship (FPU) from the Ministerio de Educación y Ciencia. The CBMSO receives an institutional grant from Fundación Ramón Arece

Classical Singularities In Chaotic Atom-Surface Scattering

In this paper we show that the diffraction condition for the scattering of atoms from surfaces leads to the appearance of a distinct type of classical singularity. Moreover, it is also shown that the onset of classical trapping or classical chaos is closely related to the bifurcation set of the diffraction-order function around the surface points presenting the rainbow effect. As an illustration of this dynamic, application to the scattering of He atoms by the stepped Cu(115) surface is presented using both a hard corrugated one-dimensional wall and a soft corrugated Morse potential

Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment

The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action, trajectories and loci of transit times are developed in the region near the two point sources. The trajectory through any point in Euclidian 3-space also passes simultaneously through both point sources.Comment: 12 pages LaTeX2e, 9 figures. Typos corrected. Author's final submission. A companion paper to "Interference, reduced action, and trajectories", quant-ph/0605120. Keywords: interference, Young's experiment, entanglement, nonlocality, trajectory representation, determinis

Dynamics of quantum trajectories in chaotic systems

Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically chaotic system, a situation in which scars are known to play a very important role. We find that the topologies of the quantum orbits are much more complicated than that of the scarring and associated periodic orbits, since the former have quantum interference built in. Thus scar wave functions are necessary to analyze the corresponding dynamics. Moreover, these topologies imply different return routes to the vicinity of the initial positions, and this reflects in the existence of different contributions in each peak of the survival probability function.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter

Trade-offs and Noise Tolerance in Signal Detection by Genetic Circuits

Genetic circuits can implement elaborated tasks of amplitude or frequency signal detection. What type of constraints could circuits experience in the performance of these tasks, and how are they affected by molecular noise? Here, we consider a simple detection process–a signal acting on a two-component module–to analyze these issues. We show that the presence of a feedback interaction in the detection module imposes a trade-off on amplitude and frequency detection, whose intensity depends on feedback strength. A direct interaction between the signal and the output species, in a type of feed-forward loop architecture, greatly modifies these trade-offs. Indeed, we observe that coherent feed-forward loops can act simultaneously as good frequency and amplitude noise-tolerant detectors. Alternatively, incoherent feed-forward loop structures can work as high-pass filters improving high frequency detection, and reaching noise tolerance by means of noise filtering. Analysis of experimental data from several specific coherent and incoherent feed-forward loops shows that these properties can be realized in a natural context. Overall, our results emphasize the limits imposed by circuit structure on its characteristic stimulus response, the functional plasticity of coherent feed-forward loops, and the seemingly paradoxical advantage of improving signal detection with noisy circuit components

Multistable Decision Switches for Flexible Control of Epigenetic Differentiation

It is now recognized that molecular circuits with positive feedback can induce two different gene expression states (bistability) under the very same cellular conditions. Whether, and how, cells make use of the coexistence of a larger number of stable states (multistability) is however largely unknown. Here, we first examine how autoregulation, a common attribute of genetic master regulators, facilitates multistability in two-component circuits. A systematic exploration of these modules' parameter space reveals two classes of molecular switches, involving transitions in bistable (progression switches) or multistable (decision switches) regimes. We demonstrate the potential of decision switches for multifaceted stimulus processing, including strength, duration, and flexible discrimination. These tasks enhance response specificity, help to store short-term memories of recent signaling events, stabilize transient gene expression, and enable stochastic fate commitment. The relevance of these circuits is further supported by biological data, because we find them in numerous developmental scenarios. Indeed, many of the presented information-processing features of decision switches could ultimately demonstrate a more flexible control of epigenetic differentiation

Speed-Dependent Cellular Decision Making in Nonequilibrium Genetic Circuits

Despite being governed by the principles of nonequilibrium transitions, gene expression dynamics underlying cell fate decision is poorly understood. In particular, the effect of signaling speed on cellular decision making is still unclear. Here we show that the decision between alternative cell fates, in a structurally symmetric circuit, can be biased depending on the speed at which the system is forced to go through the decision point. The circuit consists of two mutually inhibiting and self-activating genes, forced by two external signals with identical stationary values but different transient times. Under these conditions, slow passage through the decision point leads to a consistently biased decision due to the transient signaling asymmetry, whereas fast passage reduces and eventually eliminates the switch imbalance. The effect is robust to noise and shows that dynamic bifurcations, well known in nonequilibrium physics, are important for the control of genetic circuits