Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques

In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank methods, the proposed algorithm tracks the optimal point in the sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov subspace, even when the estimated statistics become erroneous (e.g., due to sudden changes of environments). Therefore, compared with those existing methods, the proposed algorithm is more suited to adaptive filtering applications. The algorithm is analyzed based on a modified version of the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for the interference suppression problem in code-division multiple-access (CDMA) systems as well as for simple system identification problems.Comment: 10 figures. In IEEE Transactions on Signal Processing, 201

Precision Measurements Using Squeezed Spin States via Two-axis Counter-twisting Interactions

We show that the two-axis counter twisting interaction squeezes a coherent spin state into three states of interest in quantum information, namely, the twin-Fock state, the equally-weighted superposition state, and the state that achieves the Heisenberg limit of optimal sensitivity defined by the Cramer-Rao inequality in addition to the well-known Heisenberg-limited state of spin fluctuations.Comment: 5 pages, 3 figure

A Quantum Analogue of the Jarzynski Equality

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To confirm its validity in a practical situation, we also investigate an open quantum system that is a spin 1/2 system with a scanning magnetic field interacting with a thermal heat bath. As a result, we find that the quantum analogue functions well.Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000

A quantum version of free energy - irreversible work relations

We give a quantum version of the Jarzynski relation between the distribution of work done over a certain time-interval on a system and the difference of equilibrium free energies. The main new ingredient is the identification of work depending on the quantum history of the system and the proper definition of various quantum ensembles over which the averages should be made. We also discuss a number of different regimes that have been considered by other authors and which are unified in the present set-up. In all cases, and quantum or classical, it is a general relation between heat and time-reversal that makes the Jarzynski relation so universally valid

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Implementation of screened hybrid functionals based on the Yukawa potential within the LAPW basis set

The implementation of screened hybrid functionals into the WIEN2k code, which is based on the LAPW basis set, is reported. The Hartree-Fock exchange energy and potential are screened by means of the Yukawa potential as proposed by Bylander and Kleinman [Phys. Rev. B 41, 7868 (1990)] for the calculation of the electronic structure of solids with the screened-exchange local density approximation. Details of the formalism, which is based on the method of Massidda, Posternak, and Baldereschi [Phys. Rev. B 48, 5058 (1993)] for the unscreened Hartree-Fock exchange are given. The results for the transition-energy and structural properties of several test cases are presented. Results of calculations of the Cu electric-field gradient in Cu2O are also presented, and it is shown that the hybrid functionals are much more accurate than the standard local-density or generalized gradient approximations

Recent advances in the theory of nuclear forces

After a brief historical review, we present recent progress in our understanding of nuclear forces in terms of chiral effective field theory.Comment: 6 pages, 2 figures; talk at International Symposium on Correlations Dynamics in Nuclei, University of Tokyo, Japan, 31 January-4 February, 200

Fluctuating work in coherent quantum systems: proposals and limitations

One of the most important goals in quantum thermodynamics is to demonstrate advantages of thermodynamic protocols over their classical counterparts. For that, it is necessary to (i) develop theoretical tools and experimental set-ups to deal with quantum coherence in thermodynamic contexts, and to (ii) elucidate which properties are genuinely quantum in a thermodynamic process. In this short review, we discuss proposals to define and measure work fluctuations that allow to capture quantum interference phenomena. We also discuss fundamental limitations arising due to measurement back-action, as well as connections between work distributions and quantum contextuality. We hope the different results summarised here motivate further research on the role of quantum phenomena in thermodynamics.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing). Second version: Misspell in the title correcte

Fundamentals of Traffic Flow

From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized for the specification of some fundamental relations of traffic flow and compared with existing traffic theories.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm