Axiomatic Digital Topology

The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3n\"i1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested

A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio

Echoes in classical dynamical systems

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.

Tidal controls on trace gas dynamics in a seagrass meadow of the Ria Formosa lagoon (southern Portugal)

Coastal zones are important source regions for a variety of trace gases, including halocarbons and sulfur-bearing species. While salt marshes, macroalgae and phyto-plankton communities have been intensively studied, little is known about trace gas fluxes in seagrass meadows. Here we report results of a newly developed dynamic flux chamber system that can be deployed in intertidal areas over full tidal cycles allowing for highly time-resolved measurements. The fluxes of CO2, methane (CH4) and a range of volatile organic compounds (VOCs) showed a complex dynamic mediated by tide and light. In contrast to most previous studies, our data indicate significantly enhanced fluxes during tidal immersion relative to periods of air exposure. Short emission peaks occurred with onset of the feeder current at the sampling site. We suggest an overall strong effect of advective transport processes to explain the elevated fluxes during tidal immersion. Many emission estimates from tidally influenced coastal areas still rely on measurements carried out during low tide only. Hence, our results may have significant implications for budgeting trace gases in coastal areas. This dynamic flux chamber system provides intensive time series data of community respiration (at night) and net community production (during the day) of shallow coastal systems.German Federal Ministry of Education and Research (BMBF) [03F0611E, 03F0662E]; EU FP7 ASSEMBLE research infrastructure initiative

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.Comment: 6 pages, 2 figure

Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let

Lagrangian tracers on a surface flow: the role of time correlations

Finite time correlations of the velocity in a surface flow are found to be important for the formation of clusters of Lagrangian tracers. The degree of clustering characterized by the Lyapunov spectrum of the flow is numerically shown to be in qualitative agreement with the predictions for the white-in-time compressible Kraichnan flow, but to deviate quantitatively. For intermediate values of compressibility the clustering is surprisingly weakened by time correlations.Comment: 4 pages, 5 figures, to be published in PR

Chaos and quantum-nondemolition measurements

The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ‘‘deterministic randomness’’ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity

Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach

Previous work [Gong and Brumer, Phys. Rev. Lett., 97, 240602 (2006)] motivates this study as to how asymmetry-driven quantum ratchet effects can persist despite a corresponding fully chaotic classical phase space. A simple perspective of ratchet dynamics, based on the Heisenberg picture, is introduced. We show that ratchet effects are in principle of common origin in classical and quantum mechanics, though full chaos suppresses these effects in the former but not necessarily the latter. The relationship between ratchet effects and coherent dynamical control is noted.Comment: 21 pages, 7 figures, to appear in Phys. Rev.

Symmetry Decomposition of Chaotic Dynamics

Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations in turn reduce the labor and improve the convergence of cycle expansions for classical and quantum spectra associated with the flow. In this paper the general formalism is developed, with the $N$-disk pinball model used as a concrete example and a series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01