The asymptotic spectrum of the EWMA covariance estimator

The exponentially weighted moving average (EWMA) covariance estimator is a standard estimator for financial time series, and its spectrum can be used for so-called random matrix filtering. Random matrix filtering using the spectrum of the sample covariance matrix is an established tool in finance and signal detection and the EWMA spectrum can be used analogously. In this paper, the asymptotic spectrum of the EWMA covariance estimator is calculated using the Mar?enko-Pastur theorem. Equations for the spectrum and the boundaries of the support of the spectrum are obtained and solved numerically. The spectrum is compared with covariance estimates using simulated i.i.d. data and log-returns from a subset of stocks from the S&P 500. The behaviour of the EWMA estimator in this limited empirical study is similar to the results in previous studies of sample covariance matrices. Correlations in the data are found to only affect a small part of the EWMA spectrum, suggesting that a large part may be filtered out.     

Directional tunneling escape from nearly spherical optical resonators

We report the surprising observation of directional tunneling escape from nearly spherical fused-silica optical resonators, in which most of the phase space is filled with nonchaotic regular trajectories. Experimental and theoretical studies of the dependence of the far-field emission pattern on both the degree of deformation and the excitation condition show that nonperturbative phase-space structures in the internal ray dynamics profoundly affect tunneling leakage of the whispering-gallery modes.     

Programmable networks for quantum algorithms

The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there have been no standard ways to uniformly generate whole classes of N-qubit gates. We develop a method to generate arbitrary controlled phase-shift operations with a single network of one-qubit and two-qubit operations. This kind of network can be adapted to various physical implementations of quantum computing and is suitable to realize the Deutsch-Jozsa algorithm as well as Grover's search algorithm.     

Non-Abelian holonomies,charge pumping,and quantum computation with Josephson junctions

Non-Abelian holonomies can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the non-Abelian operations are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.     

Implications of using approximate Bloch-McConnell equations in NMR analyses of chemically exchanging systems: application to the electron self-exchange of plastocyanin

The validity of a series of approximate solutions of the Bloch-McConnell equations normally applied in the analyses of chemically exchanging systems is evaluated, using the electron self-exchange (ESE) in the blue copper protein plastocyanin from Anabaena variabilis as an example. The evaluation is based on a comparison with the results of a complete analysis of the NMR signals of chemically exchanging nuclei that allows an independent and accurate determination of all the involved parameters. The complete analysis is based on the general solution of the Bloch-McConnell equations. It includes a simultaneous analysis of the chemical shift, and the transverse and longitudinal relaxation rates of the observed nuclei as well as the variation of these parameters with the molar fractions of the exchanging species and the rate of the chemical exchange process. The linear prediction model method was used in the data analysis to achieve the highest possible precision. Surprisingly, it is found that the fast exchange condition may not be fulfilled even in cases where a single exchange-averaged NMR signal is observed, and the Larmor frequency and relaxation rates depend linearly on the molar fractions of the exchanging species. In such cases the use of approximate solutions in the analysis of the transverse relaxation rates and the pseudo-contact shifts can lead to erroneous results. In limiting cases close to the fast exchange and slow exchange regimes correct values of some of the parameters can be obtained using the second order approximate solution of the Bloch-McConnell equations. In contrast, the complete analysis of the NMR signals results in an accurate determination of the exchange rates and the NMR parameters of the exchanging sites. This, in turn, can provide information about the structure and function of a protein undergoing chemically exchange. For the investigated plastocyanin the complete analysis results in an accurate determination of the paramagnetic enhancement of the nuclear relaxation rates, the paramagnetic chemical shift, the electron relaxation rate, the electron self-exchange rate, and the distances between the nuclei and the paramagnetic metal ion, viz. the Cu2+ ion.     

Energy transfer in self-assembled [N]-acene fibers involving > or =100 donors per acceptor

Anthracene derivatives self-assemble into fibers with a high molecular order, as is evidenced by probing the structure with energy-trapping tetracene analogues. Efficient energy transfer processes involving tens to hundreds of donors per acceptor and high emission quantum yields are outstanding characteristics displayed in these self-assembled fibers.     

Approximation of Integral Operators by Variable-Order Interpolation

Summary. We employ a data-sparse, recursive matrix representation, so-called -matrices, for the efficient treatment of discretized integral operators. We obtain this format using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones. The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the matrix-vector multiplication. We present an error analysis for integral operators of order zero. In particular, we show that the optimal convergence (h) is retained for the classical double layer potential discretized with piecewise constant functions.Corrigendum This revised version was published online in February 2005 due to typesetting mistakes in the author correction process.     

Coevolutionary dynamics: from finite to infinite populations

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.     

Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation

We present phase-resolved pulse propagation measurements that allow us to fully describe the transition between several light-matter interaction regimes. The complete range from linear excitation to the breakdown of the photonic bandgap on to self-induced transmission and self-phase modulation is studied on a high-quality multiple-quantum-well Bragg structure. An improved fast-scanning cross-correlation frequency-resolved optical gating setup is applied to retrieve the pulse phase with an excellent signal-to-noise ratio. Calculations using the semiconductor Maxwell-Bloch equations show qualitative agreement with the experimental findings.     

Carrier envelope phase noise in stabilized amplifier systems

At present most laser systems for generating phase-stabilized high-energy pulses are chirped pulse amplifier systems that involve the selection and subsequent amplification of pulses from a phase-stabilized seed oscillator. We investigate the effect of the picking process on the carrier envelope phase stability and how the phase noise of the picked pulse sequence can be estimated from the phase noise properties of the seed oscillator. All noise components from the original pulse train above the picking frequency are aliased into the picked pulse train and therefore cannot be neglected.