Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session Z13: Statistical and Nonlinear Physics II |
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Sponsoring Units: GSNP Chair: M. Kaufman, Cleveland State University Room: B112 |
Friday, March 19, 2010 11:15AM - 11:27AM |
Z13.00001: Prediction, Retrodiction, and the Amount of Information Stored in the Present Christopher J. Ellison, John R. Mahoney, James P. Crutchfield We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically, computationally, and conceptually. Mathematically, we prove that the excess entropy---a familiar measure of organization in complex systems---is the mutual information not only between the past and future, but also between the predictive and retrodictive causal states. Practically, we exploit the connection between prediction and retrodiction to directly calculate the excess entropy. Conceptually, these lead one to discover new system measures for stochastic dynamical systems: crypticity (information accessibility) and causal irreversibility. Ultimately, we introduce a time-symmetric representation that unifies all of these quantities, compressing the two directional representations into one. The resulting compression offers a new conception of the amount of information stored in the present. [Preview Abstract] |
Friday, March 19, 2010 11:27AM - 11:39AM |
Z13.00002: Information Accessibility and Cryptic Processes John Mahoney, Chris Ellison, James Crutchfield We give a systematic expansion of the \emph{crypticity}--a recently introduced measure of the inaccessibility of a stationary process's internal state information. This leads to a hierarchy of \emph{k-cryptic} processes and allows us to identify finite-state processes that have infinite cryptic order--the internal state information is present across arbitrarily long, observed sequences. The crypticity expansion is exact in both the finite- and infinite-order cases. It turns out that k-crypticity is complementary to the Markovian finite-order property that describes state information in processes. One application of these results is an efficient expansion of the \emph{excess entropy}--the mutual information between a process's infinite past and infinite future--that is finite and exact for finite-order cryptic processes. [Preview Abstract] |
Friday, March 19, 2010 11:39AM - 11:51AM |
Z13.00003: ABSTRACT WITHDRAWN |
Friday, March 19, 2010 11:51AM - 12:03PM |
Z13.00004: New integro-differential diffusion equation for continuous time random walk Kwok Sau Fa, Ke-Gang Wang We present a new integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution. [Preview Abstract] |
Friday, March 19, 2010 12:03PM - 12:15PM |
Z13.00005: Universal and non-universal properties of wave chaotic scattering systems Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven Anlage The application of random matrix theory to scattering requires introduction of system-specific information. Here, we show that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports [1]. We compare theoretical predictions with experimental results for a microwave billiard, demonstrating that the theory successfully uncovered universal statistics of wave-chaotic scattering systems [2]. These results should be broadly useful in nuclear scattering, atomic physics, quantum transport in condensed matter systems, electromagnetics, acoustics, geophysics, etc. [1] James A. Hart, T. M. Antonsen, E. Ott, "\textbf{The effect of short ray trajectories on the scattering statistics of wave chaotic systems}," \underline {Phys. Rev. E }\underline {\textbf{80}}\underline {, 041109~(2009)}. [2] Jen-Hao Yeh, \textit{et al}., \underline {arXiv:0909.2674}. [Preview Abstract] |
Friday, March 19, 2010 12:15PM - 12:27PM |
Z13.00006: Towards random matrix model of breaking the time-reversal invariance of elastic waves in chaotic cavities by feedback Oleg Antoniuk, Rudolf Sprik We developed a random matrix model to describe the statistics of resonances in an acoustic cavity with broken time-reversal invariance. Time-reversal invariance braking is achieved by connecting an amplified feedback loop between two transducers on the surface of the cavity. The model is based on approach [1] that describes time- reversal properties of the cavity without a feedback loop. Statistics of eigenvalues (nearest neighbor resonance spacing distributions and spectral rigidity) has been calculated and compared to the statistics obtained from our experimental data. Experiments have been performed on aluminum block of chaotic shape confining ultrasound waves. [1] Carsten Draeger and Mathias Fink, One-channel time- reversal in chaotic cavities: Theoretical limits, Journal of Acoustical Society of America, vol. 105, Nr. 2, pp. 611-617 (1999) [Preview Abstract] |
Friday, March 19, 2010 12:27PM - 12:39PM |
Z13.00007: Sensing Small Changes in a Wave Chaotic Scattering System Biniyam Taddese, James Hart, Thomas Antonsen, Edward Ott, Steven Anlage We had demonstrated a new remote sensor scheme by applying the wave mechanical concept of fidelity loss to classical waves. The sensor makes explicit use of time- reversal invariance and spatial reciprocity in a wave chaotic system to sensitively and remotely measure the presence of small perturbations to the system [1]. The loss of fidelity is measured through a classical wave-analog of the Loschmidt echo by employing a single-channel time-reversal mirror to rebroadcast a probe signal into the perturbed system. We now compare and contrast the detection power and computational efficiency of our sensor with other techniques such as correlation and/or mutual information of probing signals. We also introduce the use of exponential amplification of the probe signal to partially overcome the effects of propagation losses. It is demonstrated that exponential amplification can be used to vary the spatial range of sensitivity to perturbations, and the extent to which the spatial range of the sensors can be varied. Experimental results are presented for the acoustic version of the sensing techniques under study. \\[4pt] [1] B. T. Taddese, \textit{et al}., Appl. Phys. Lett. 95, 114103 (2009) (http://link.aip.org/link/?APPLAB/95/114103/1) [Preview Abstract] |
Friday, March 19, 2010 12:39PM - 12:51PM |
Z13.00008: Simulations of fractal electronic circuits R.D. Montgomery, M.S. Fairbanks, S.A. Brown, R.P. Taylor Many natural structures make use of fractal geometry's inherent properties, which can include very high surface area to volume ratios, connectivity, and dispersion. Recent research and technological applications have begun to leverage these same properties in artificial structures including antenna and capacitor designs~[1]. Here we present DC electrical simulations as a first step toward circuits in which the components themselves have fractal character. Our results show that such `fractal circuits' produce complicated differential resistance curves (in response to a simple electrostatic gating scheme) that is unique to the underlying fractal geometry. Finally, we will discuss potential applications of these devices as well as candidate systems for fractal circuit fabrication. \\[4pt] [1] Cohen, N. L. \emph{Communications Quarterly} Summer, 9 (1995).; Samavati, H., Hajimiri, A., Shahani, A. R., et al. \emph{IEEE J Sol St Circ} 33 2035 - 2041 (1998). [Preview Abstract] |
Friday, March 19, 2010 12:51PM - 1:03PM |
Z13.00009: Simple Autonomous Chaotic Circuits Jessica Piper, J. Sprott Over the last several decades, numerous electronic circuits exhibiting chaos have been proposed. Non-autonomous circuits with as few as two components have been developed. However, the operation of such circuits relies on the non-ideal behavior of the devices used, and therefore the circuit equations can be quite complex. In this paper, we present two simple autonomous chaotic circuits using only opamps and linear passive components. The circuits each use one opamp as a comparator, to provide a signum nonlinearity. The chaotic behavior is robust, and independent of nonlinearities in the passive components. Moreover, the circuit equations are among the algebraically simplest chaotic systems yet constructed. [Preview Abstract] |
Friday, March 19, 2010 1:03PM - 1:15PM |
Z13.00010: $\cal{PT}$ -symmetry Wave Chaos Carl T. West, Tsampikos Kottos, Tomaz Prosen We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time ${\cal PT}$ symmetry. For a value $\gamma_{\cal PT}$ of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for $\gamma_{\cal PT}$, and show that chaos assists the exact ${\cal PT}$-phase. Our results will have applications to the design of optical elements with ${\cal PT}$-symmetry. [Preview Abstract] |
Friday, March 19, 2010 1:15PM - 1:27PM |
Z13.00011: Optical synthetic materials with local Parity-Time symmetry Mei Chai Zheng, Demetrios Christodoulides, Ragnar Fleischmann, Tsampikos Kottos We discuss the eigenvalue and eigenvector properties of a class of optical synthetic materials that are described by effective non-hermitian Hamiltonians with Parity-Time symmetry. The building blocks of such systems are coupled dimers with judiciously tailored internal structure such that one element of the dimer incorporates losses while the other balanced these losses with a gain. We show that these systems have a robust exact PT-phase (i.e. parameter regime of the gain/loss coefficient where the spectrum is real), even if the inter-dimer and intra-dimer couplings are random. We further analyze the beam dynamics in such optical lattices and show non-reciprocal diffraction beam evolution. [Preview Abstract] |
Friday, March 19, 2010 1:27PM - 1:39PM |
Z13.00012: A new test for missing levles using the $\Delta_3(L)$ statistic Declan Mulhall The $\Delta_3(L)$ statistic of Random Matrix Theory is a measure of how a spectrum deviates from the equidistant harmonic oscillator spectrum. While it is usually used as a signature of quantum chaos, in this work it is used to gauge the incompleteness of an experimental spectrum. Two approaches are presented. In the first, the $\Delta_3(L)$ statistic extracted from the experimental data is compared to randomly depleted spectra in numerical simulations. The second approach depends on the fact that $\Delta_3(L)$ is the mean value of a quantity that is evaluated many times over the spectrum. These values are not statistically independent, and their distribution is non trivial. In this second approach this distribution of numbers (whose average is $\Delta_3(L)$) is parametrized, and a maximum likelihood method is then developed as a tool to detect missing levels. [Preview Abstract] |
Friday, March 19, 2010 1:39PM - 1:51PM |
Z13.00013: Coupled parallel totally asymmetric exclusion processes with extended particles Konstantinos Tsekouras, Anatoly Kolomeisky A complex system consisting of coupled parallel totally asymmetric processes (TASEP) with extended particles is investigated theoretically. Stationary-state properties and phase diagrams are obtained using several approximate methods. We find that the maximum-current phase is very well described by the Tonks gas lattice-based treatment as in the case of the extended-particle single-lane TASEP. However, although the probability balance treatment used in that case for the low and high-density phases yields acceptable results for the low-density phase, it completely fails for the high-density phase in our system. We show that this discrepancy is a result of the coupling and demonstrate that a simple ansatz derived from the single-lane single-particle TASEP restores consistency to the theory. We validate all theoretical predictions via extensive Monte-Carlo simulations: agreement between them and theory is mostly excellent except for the low density/maximum-current phase transition which the theory consistently underestimates. It is shown this disagreement is a result of very slow current saturation with increased exit rate in the relevant region of the phase diagram. [Preview Abstract] |
Friday, March 19, 2010 1:51PM - 2:03PM |
Z13.00014: Newtonian trajectories: a powerful tool for solving quantum dynamics Fons Brosens, Wim Magnus Since Ehrenfest's theorem, the role and importance of the classical paths in quantum dynamics have been examined by several means, and nowadays stochastic versions of the classical equation of motion are being investigated. Along this line, we show that the classical equations of motion provide a solution to quantum dynamics, if appropriately incorporated in the Wigner distribution function, exactly reformulated in a type of Boltzmann equation. Also the quantum-mechanical features of thermal equilibrium are studied in this framework. Even fermions and bosons can be treated on the basis of classical paths, provided the initial distribution function is constructed in agreement with the identical-particle statistics. [Preview Abstract] |
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