Intrinsic Decoherence Dynamics in Smooth Hamiltonian Systems: Quantum-classical Correspondence

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer new insights into decoherence, dynamics of quantum entanglement, and quantum chaos.Comment: 12 pages, 7 figures, to appear in Physical Review

Large Scale Cross-Correlations in Internet Traffic

The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.Comment: 7 pages, 6 figures, final versio

Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime

Power-law random banded unitary matrices (PRBUM), whose matrix elements decay in a power-law fashion, were recently proposed to model the critical statistics of the Floquet eigenstates of periodically driven quantum systems. In this work, we numerically study in detail the statistical properties of PRBUM ensembles in the delocalization-localization transition regime. In particular, implications of the delocalization-localization transition for the fractal dimension of the eigenvectors, for the distribution function of the eigenvector components, and for the nearest neighbor spacing statistics of the eigenphases are examined. On the one hand, our results further indicate that a PRBUM ensemble can serve as a unitary analog of the power-law random Hermitian matrix model for Anderson transition. On the other hand, some statistical features unseen before are found from PRBUM. For example, the dependence of the fractal dimension of the eigenvectors of PRBUM upon one ensemble parameter displays features that are quite different from that for the power-law random Hermitian matrix model. Furthermore, in the time-reversal symmetric case the nearest neighbor spacing distribution of PRBUM eigenphases is found to obey a semi-Poisson distribution for a broad range, but display an anomalous level repulsion in the absence of time-reversal symmetry.Comment: 10 pages + 13 fig

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

Application of K-Means and Genetic Algorithms for Dimension Reduction by Integrating SVM for Diabetes Diagnosis

AbstractVast amount of data available in health care industry is difficult to handle, hence mining is necessary to find the necessary pattern and relationship among the features available. Medical data mining is one major research area where evolutionary algorithms and clustering algorithms play a vital role. In this research work, K-Means is used for removing the noisy data and genetic algorithms for finding the optimal set of features with Support Vector Machine (SVM) as classifier for classification. The experimental result proves that, the proposed model has attained an average accuracy of 98.79% for reduced dataset of Pima Indians Diabetes from UCI repository. It also shows that the proposed method has attained better results compared to modified K-Means clustering based data preparation method with SVM classifier (96.71%) as described in the literatur

Synchronization of Coupled Map Lattice using Delayed Variable Feedback

We apply the method of variable feedback to obtain complete synchronization in a coupled map lattice. The conditions under which such a synchronization is possible are obtained analytically. We show that synchronization is robust against noise and parameter mismatches. This method leads to synchronized state quite rapidly and we discuss its applications for near-real-time multi-channel communications

Genetic Programming Based Approach for Synchronization with Parameter Mismatches in EEG

Effects of parameter mismatches in synchronized time series are studied first for an analytical non-linear dynamical system (coupled logistic map, CLM) and then in a real system (Electroencephalograph (EEG) signals). The internal system parameters derived from GP analysis are shown to be quite effective in understanding aspects of synchronization and non-synchronization in the two systems considered. In particular, GP is also successful in generating the CLM coupled equations to a very good accuracy with reasonable multi-step predictions. It is shown that synchronization in the above two systems is well understood in terms of parameter mismatches in the system equations derived by GP approach

Evolving networks with bimodal degree distribution

Networks with bimodal degree distribution are most robust to targeted and random attacks. We present a model for constructing a network with bimodal degree distribution. The procedure adopted is to add nodes to the network with a probability p and delete the links between nodes with probability (1 − p). We introduce an additional constraint in the process through an immunity score, which controls the dynamics of the growth process based on the feedback value of the last few time steps. This results in bimodal nature for the degree distribution. We study the standard quantities which characterize the networks, like average path length and clustering coefficient in the context of our growth process and show that the resultant network is in the small world family. It is interesting to note that bimodality in degree distribution is an emergent phenomenon

Laminated High-Aspect-Ratio Microstructures in a Conventional CMOS Process

Electrostatically actuated microstructures with high-aspect-ratio laminated-beam suspensions have been fabricated using conventional CMOS processing followed by a sequence of maskless dry-etching steps. Laminated structures are etched out of the CMOS silicon oxide, silicon nitride, and aluminum layers. The key to the process is use of the CMOS metallization as an etch-resistant mask to define the microstructures. A minimum beam width and gap of 1.2 μm and maximum beam thickness of 4.8 μm are fabricated in a 0.8 μm 3-metal CMOS process available through MOSIS. Structural features will scale in size as the CMOS technology improves. An effective Young's modulus of 63 GPa is extracted from resonant frequency measurements. Cantilevered structures slightly curl up with a radius of curvature of about 4.2 mm. Multi-conductor electrostatic micromechanisms, such as self-actuating springs and nested comb-drive lateral resonators, are successfully produced. Self-actuating springs are self-aligned multi-conductor electrostatic microactuators that are insensitive to curl. The resonance amplitude is 1 μm for an 107 μm-wide×109 μm-long spring with an applied 11 V ac signal. Finite-element simulation using the extracted value for Young's modulus predicts the resonant frequency of the springs to within 6% of the measured value