Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

Tables of Bessel-Clifford functions of orders zero and one.

Mode of access: Internet.

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

ACM Computing Classification System (1998): G.1.2.

Superregular matrices and applications to convolutional codes

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature.

Splitting of the zero-energy edge states in bilayer graphene

Bilayer graphene nanoribbons with zigzag termination are studied within the tight-binding model. We also include single-site electron-electron interactions via the Hubbard model within the unrestricted Hartree-Fock approach. We show that either the interactions between the outermost edge atoms or the presence of a magnetic order can cause a splitting of the zero-energy edge states. Two kinds of edge alignments are considered. For one kind of edge alignment (?) the system is nonmagnetic unless the Hubbard parameter U becomes greater than a critical value Uc. For the other kind of edge alignment (?) the system is magnetic for any U>0. Our results agree very well with ab initio density functional theory calculations.

Conservation laws, integrability, and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.

Spin-charge coupling in quantum wires at zero magnetic field

We discuss an approximation for the dynamic charge response of nonlinear spin-1/2 Luttinger liquids in the limit of small momentum. Besides accounting for the broadening of the charge peak due to two-holon excitations, the nonlinearity of the dispersion gives rise to a two-spinon peak, which at zero temperature has an asymmetric line shape. At finite temperature the spin peak is broadened by diffusion. As an application, we discuss the density and temperature dependence of the Coulomb drag resistivity due to long-wavelength scattering between quantum wires.

Universal zero-bias conductance through a quantum wire side-coupled to a quantum dot

A numerical renormalization-group study of the conductance through a quantum wire containing noninteracting electrons side-coupled to a quantum dot is reported. The temperature and the dot-energy dependence of the conductance are examined in the light of a recently derived linear mapping between the temperature-dependent conductance and the universal function describing the conductance for the symmetric Anderson model of a quantum wire with an embedded quantum dot. Two conduction paths, one traversing the wire, the other a bypass through the quantum dot, are identified. A gate potential applied to the quantum wire is shown to control the current through the bypass. When the potential favors transport through the wire, the conductance in the Kondo regime rises from nearly zero at low temperatures to nearly ballistic at high temperatures. When it favors the dot, the pattern is reversed: the conductance decays from nearly ballistic to nearly zero. When comparable currents flow through the two channels, the conductance is nearly temperature independent in the Kondo regime, and Fano antiresonances in the fixed-temperature plots of the conductance as a function of the dot-energy signal interference between them. Throughout the Kondo regime and, at low temperatures, even in the mixed-valence regime, the numerical data are in excellent agreement with the universal mapping.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Can we make a Bohmian electron reach the speed of light, at least for one instant?

In Bohmian mechanics, a version of quantum mechanics that ascribes world lines to electrons, we can meaningfully ask about an electron's instantaneous speed relative to a given inertial frame. Interestingly, according to the relativistic version of Bohmian mechanics using the Dirac equation, a massive particle's speed is less than or equal to the speed of light, but not necessarily less. That is, there are situations in which the particle actually reaches the speed of light-a very nonclassical behavior. That leads us to the question of whether such situations can be arranged experimentally. We prove a theorem, Theorem 5, implying that for generic initial wave functions the probability that the particle ever reaches the speed of light, even if at only one point in time, is zero. We conclude that the answer to the question is no. Since a trajectory reaches the speed of light whenever the quantum probability current (psi) over bar gamma(mu)psi is a lightlike 4-vector, our analysis concerns the current vector field of a generic wave function and may thus be of interest also independently of Bohmian mechanics. The fact that the current is never spacelike has been used to argue against the possibility of faster-than-light tunneling through a barrier, a somewhat similar question. Theorem 5, as well as a more general version provided by Theorem 6, are also interesting in their own right. They concern a certain property of a function psi : R(4) -> C(4) that is crucial to the question of reaching the speed of light, namely being transverse to a certain submanifold of C(4) along a given compact subset of space-time. While it follows from the known transversality theorem of differential topology that this property is generic among smooth functions psi : R(4) -> C(4), Theorem 5 asserts that it is also generic among smooth solutions of the Dirac equation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3520529]

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.

Integrable Kondo impurities in the one-dimensional supersymmetric extended Hubbard model

An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local moments of the impurities are presented as a non-trivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.